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Find regex pattern match string have multiple condition?

I have some strings formatted as follows:
1=case1,case2,..caseN;2=case1,..,caseN;3=case1, ..,caseN
Note: comma ";" is used to separate cases and case1, case2 are anything like strings, number doesn't matter their type.
I want to find regex pattern to match string
1=home,house;2=abc;3=2019,2021
however, it will not match the following:
1=home,;2=abc;3=2019,2021 (Excess comma mark at case 1)
1=;2=abc,2012;3= (must 1=..; not 1=;)
1=home,age;2 (must 2=.. not 2)
2=home;;3=sea (must ;3 not ;;3)
4=flower;k3=sea (must 3= , not k3)
I tried with the pattern: (\d+={1}[^;]+;). However, it will match if the backstring is not.
Please show me the way.
Many thanks!

Maybe this pattern helps you out:
^\b(?:(?:^|;)\d+=[^,;]+(?:,[^,;]+)*)+$
See the Online Demo
^ - Start string ancor.
\b - Word-boundary.
(?: - Opening 1st non-capture group.
(?:- Opening 2nd non-capture group.
^|; - Alternation between start string ancor or semi-colon.
) - Closing 2nd non-capture group.
\d+= - One or more digits followed by a =.
[^,;]+ - Negated character class, any character other than comma or semicolon one or more times.
(?: - Opening 3rd non-capture group.
, - A comma.
[^,;]+ - Negated character class, any character other than comma or semicolon one or more times.
)* - Close 3rd non-capture group and make it match zero or more times.
)+ - Close 1st non-capture group and make sure it's matches one or more times.
$ - End string ancor.
Note: I went with a negated character class since you mentioned "case1, case2 are anything like strings, number doesn't matter their type", therefor I read there can be spaces, special characters or any kind other than comma and semicolon.

This works on regex101
^(?:\d=(?:\w{1,},)*(?:\w{1,});)*(?:\d=(?:\w{1,},)*\w{1,})$

^(?:\d+=[a-z\d]+(?:,[a-z\d]+)*(?:;|$))+$
Demo
^ : match beginning of string
(?: : begin nc group
\d+=[a-z\d]+ : match 1+ digits, then '=' then 1+ lc letters or digits
(?:,[a-z\d]+) : match ',' then 1+ lc letters or digits in nc group
* : execute nc group 0+ times
(?:;|$) : match ';' or end of string
)+ : end nc group and execute 1+ times
$ : match end of string

I don't know if c# supports recursive pattern, but, if it does, use:
^(\d+=\w+(?:,\w+)*)(?:;(?1))*$
if it doesn't:
^\d+=\w+(?:,\w+)*(?:;\d+=\w+(?:,\w+)*)*$
Demo & explanation

How to match a string between <>?

I tried \w+\:(\w+\-?\.?(\d+)?) but that is not correct
I have following text
<staticText:HelloWorld>_<xmlNode:Node.03>_<date:yyy-MM-dd>_<time:HH-mm-ss-fff>
The end result I want is something like the following
["staticText:HelloWorld", "xmlNode:Node.03","date:yyy-MM-dd","time:HH-mm-ss-fff"]

You could use the following regex.
<(.*?)>
Then have a look at how groups work to retrieve the result.
Regex rx = new Regex("<(.*?)>");
string text = "<staticText:HelloWorld>_<xmlNode:Node.03>_<date:yyy-MM-dd>_<time:HH-mm-ss-fff>";
MatchCollection matches = rx.Matches(text);
Console.WriteLine(matches.Count);
foreach(Match match in matches){
var groups = match.Groups;
Console.WriteLine(groups[1]);
}

This line should be able to match the content:
<(.*?)>
It will catch the arrows at the end which you don't seem to want, but you could remove them after words without regex.
You should consider a website like https://regexr.com - it helps exponentially in writing regex by allowing you to paste your cases and see how it works with them.

Matches any string within the <>. Hope this helps.
<(.*?)>

Your pattern does not match the 3rd and the 4th part of the example data because in this part \w+\-?\.?(\d+)? the dash and the digits match only once and are not repeated.
For your example data, you might use a character class [\w.-]+to match the part after the colon to make the match a bit more broad:
<(\w+\:[\w.-]+)>
Regex demo | C# demo
Or to make it more specific, specify a pattern for either the Node.03 part and for the year month date hour etc parts using a repeated pattern.
<(\w+\:\w+(?:\.\d+|\d+(?:-\d+)+)?)>
Explanation
< Match <
( Capturing group
\w+\:\w+ Match 1+ word chars, : and 1+ word chars
(?: Non capturing group
\.\d+ Match . and 1+ digits
| Or
\d+(?:-\d+)+ Match 1+ digits and repeat 1+ times matching - and 1+ digits
)? Close non capturing group and make it optional
) Close capturing group
>
Regex demo | C# Demo

C# Regular Expression Help - grouping with optional data points

Given 2 different lines I'm parsing, I need to extract the data points into regex match groups.
Example Line 1:
Header values are as follows:
DATE{space}TYPE{space}DESCR{space}VOLUME{space}RATE{space}TOTAL
[11/30/15] [CF] [DISC 1] [28270.18] [0.00150] [-42.41]
Example Line 2:
DATE{space}TYPE{space}DESCR{space}VOLUME{space}RATE{space}TOTAL
[11/30/15] [CF] [OTHER VOLUME FEES] [28186.68] [0.00008] [-2.25]
I'm using the following regex to get matches:
(?<date>^\d{1,2}[-/.]\d{1,2}[-/.]\d{1,2}[\d+])\s+(?<type>[A-Za-z]{2})\s+(?<descr>\w+\s+.*?(1))\s+.*?(?<volume>(\d+(?:\.\d+?))\s+.*?(?<rate>([0]?(\d+(?:\.\d+)?)))\s+(?<total>[-+]?\d+[.,]\d+)?.*$")
I can match the first case,but never the second case. there will always be a total, but they may NOT always be volume or rate. In addition, volume can be whole, decimal or code (e.g. "1B").
What am I missing here?
The description field is an open field and may contain "1" in it. I can have several words in it, or just 1.

Your log lines contain 6 fields, but the 4th and 5th can go missing. A common way to match optional fields is using an optional non-capturing group, (?:...)?. These groups do not make a separate memory buffers for the text they match, that is why they are useful to keep matching cleaner and more efficient.
NOTE that in .NET, there is a way to make all non-named capturing groups non-capturing by use of RegexOptions.ExplicitCapture option.
Your fixed regex mau look like
^(?<date>\d{1,2}[-/.]\d{1,2}[-/.]\d{1,2})\s+(?:(?<type>[A-Z]{2})\s+)?(?:(?<descr>\w.*?)\s+)?(?:(?<volume>\d*\.?\d+)\s+)?(?:(?<rate>\d*\.?\d+)\s+)?(?<total>[-+]?\d*[.,]?\d+)\s*$
See the .NET regex demo.
Details
^ - start of a line (when RegexOptions.Multiline is used)
(?<date>\d{1,2}[-/.]\d{1,2}[-/.]\d{1,2}) - Group "date": 1-2 digits and then 2 repetitions of -///. followed with 1-2 digits (thus, this pattern can be written as (?<date>\d{1,2}(?:[-/.]\d{1,2}){2})).
\s+ - 1 or more whitespaces
(?:(?<type>[A-Z]{2})\s+)? - an optional group matching 2 uppercase ASCII letters, captured into Group "type", and then 1+ whitespaces
(?:(?<descr>\w.*?)\s+)? - an optional group matching a word char (letter, digit or _ and some other special chars (like diacritics) followed with any 0+ chars other than a newline char LF, as few as possible, all this captured into Group "descr", and then 1+ whitespaces
(?:(?<volume>\d*\.?\d+)\s+)? - an optional group matching 0+ digits, an optional . and then 1+ digits (that is, floats or integers) captured into Group "volume", then 1+ whitespace chars
(?:(?<rate>\d*\.?\d+)\s+)? - an optional group matching a float or integer values captured into Group "rate", and then 1+ whitespace chars
(?<total>[-+]?\d*[.,]?\d+) - Group "total": an optional - or + followed with 0+ digits, an optional . or , and then 1+ digits (so, positive or negative floats or integers are matched)
\s* - any 0+ trailing whitespaces
$ - end of the line.

(?<date>^\d{1,2}[-/.]\d{1,2}[-/.]\d{1,2}[\d+])\s+(?<type>[A-Z]{2})\s+(?<descr>\w+.*?\s+)(?<volume>\d+[.]?\d+)\s+(?<rate>\d+[.]?\d+)\s+(?<total>[-+]?\d+[.,]\d+?.*$)
Yes. This is a fairly complex regex. But if you have varying spaces inside your grouping, you can use .*?\s+ to end on the last space. This seems to work nicely for all the use cases I have.
Thanks for your comments!

C# Regular Expression for x number of groups of A-Z separated by hyphen

I am trying to match the following pattern.
A minimum of 3 'groups' of alphanumeric characters separated by a hyphen.
Eg: ABC1-AB-B5-ABC1
Each group can be any number of characters long.
I have tried the following:
^(\w*(-)){3,}?$
This gives me what I want to an extent.
ABC1-AB-B5-0001 fails, and ABC1-AB-B5-0001- passes.
I don't want the trailing hyphen to be a requirement.
I can't figure out how to modify the expression.

Your ^(\w*(-)){3,}?$ pattern even allows a string like ----- because the only required pattern here is a hyphen: \w* may match 0 word chars. The - may be both leading and trailing because of that.
You may use
\A\w+(?:-\w+){2,}\z
Details:
\A - start of string
\w+ - 1+ word chars (that is, letters, digits or _ symbols)
(?:-\w+){2,} - 2 or more sequences of:
- - a single hyphen
\w+ - 1 or more word chars
\z - the very end of string.
See the regex demo.
Or, if you do not want to allow _:
\A[^\W_]+(?:-[^\W_]+){2,}\z
or to only allow ASCII letters and digits:
\A[A-Za-z0-9]+(?:-[A-Za-z0-9]+){2,}\z

It can be like this:
^\w+-\w+-\w+(-\w+)*$

^(\w+-){2,}(\w+)-?$
Matches 2+ groups separated by a hyphen, then a single group possibly terminated by a hyphen.

((?:-?\w+){3,})
Matches minimum 3 groups, optionally starting with a hyphen, thus ignoring the trailing hyphen.
Note that the \w word character also select the underscore char _ as well as 0-9 and a-z
link to demo

Regex to clean repetitions of characters

I have a pattern in the string like this:
T T and I want to T
And It can be any character from [a-z].
I have tried this Regex Example but not able to replace it.
EDIT
Like I have A Aa ar r then it should become Aar means replace any character 1st or 2nd no matter what it is.

You can use the backreferences for this.
/([a-z])\s*\1\s?/gi
Example
Some more explanation:
( begin matching group 1
[a-z] match any character from a to z
) end matching group 1
\s* match any amount of space characters
\1 match the result of matching group 1
exactly as it was again
this allows for the repition
\s? match none or one space character
this will allow to remove multiple
spaces when replacing