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how to get the child nodes and group them from a parent node

I have a XElement object that has a structure to the one below.
How would I select all the CalcConceptId children nodes from the TestResults root node where the DataPointValue attributes are different, and store them as XElements in an array/list? I want to be able to store each child as another XElement so I can loop through them and fetch out the SeriesAsOfDate and data nodes from each one.
<TestResults RSSD="123456">
<CalcConceptId Id="110" DataPointValue="10">
<SeriesAsOfDate Value="2013-07-10T00:00:00">
<Data AsOfDate="7/10/2013" ExpectedValue="1" />
<Data AsOfDate="7/3/2013" ExpectedValue="14" />
<Data AsOfDate="6/26/2013" ExpectedValue="55" />
</SeriesAsOfDate>
</CalcConceptId>
<CalcConceptId Id="110" DataPointValue="20">
<SeriesAsOfDate Value="2013-07-10T00:00:00">
<Data AsOfDate="7/10/2013" ExpectedValue="4" />
<Data AsOfDate="7/3/2013" ExpectedValue="34" />
<Data AsOfDate="6/26/2013" ExpectedValue="1" />
</SeriesAsOfDate>
</CalcConceptId>
</TestResults>

I think you want all of the CalcConceptId nodes grouped by DataPointValue but it's a little unclear what "Where the DataPointValue is different" means.
Anyway here is what I think you want...
var calcConceptIdGroupedByDataPointValue =
doc.Descendants("CalcConceptId")
.GroupBy(calcConceptId => calcConceptId.Attribute("DataPointValue"));

I'm not 100% sure... but if I get what you're asking, are you looking for this?
//assuming the XElement is called Data:
var result =
data.Elements().GroupBy(x => int.Parse(x.Attribute("DataPointValue")))
.Select(g => g.First());

Reading XML Attributes into a List

I'm new to XML and am having trouble reading my XML response back from a HttpWebResponse.
Here is the response back:
<RESPONSE version="1.2">
<RESULTS>
<AN an_type="C"
an_id="783hdryfdg56a2"
an_num="1"
an_status="100" />
<RESULTS>
</RESPONSE>
I'm looking to extract out the an_id value and save it to a list. Started doing this but seems to get an for xmlnodelist as an int but it thinks nodes["an_id"] is a string
List<int> IDs = new List<int>();
XmlDocument doc = new XmlDocument();
doc.LoadXml(returnValue);
XmlNodeList nodes = doc.SelectNodes("SEARCH_RESULTS/LOAN");
LoanIDs.Add(Convert.ToInt32(nodes["an_id"].InnerText));
Also is their a way to once the an_id's are added to a list. foreach item in the list use it as aparameter for a new xml like this:
<INPUT>
<LOGIN API_ID=""cat"" API_PASSWORD=""dog"" />
<REQUEST>
<AN an_id=""#anID"" />
<AN an_id=""#anID"" />
....foreach one in list it adds a new node with the value
</REQUEST>
</INPUT>

With xml being your string with the XML code:
var ids = XDocument.Parse(xml).
Descendants("AN").
Select(e => (string)e.Attribute("an_id")).
ToList();
However, from your sample it didn't seem that the attribute is always an integer. Are you sure about your conversion? I changed the cast of the attribute to (string) given your latest comment.
When you want to reuse the list, with current being the parent element containing the ones you want to add:
current.Add(ids.Select(i => new XElement("AN", new XAttribute("an_id", i))));

Linq - getting root descendants

The xml file is this one:
<settings y="1" x="0">
<prospect aksdj="sdf">
<image path="images/1.jpg"/>
</prospect>
<prospect aksdfasdj="safafdf">
<image path="images/2.jpg"/>
</prospect>
</settings>
I want to get both rows with the image tags.
My code is this:
XElement doc = XElement.Load(#"C:\Users\John\Desktop\File.xml");
var result = (from c in doc.Descendants("settings")
select new
{
name = c.Element("prospect").Value
}).ToList();
But, doc.Descendants("settings") is null. Why is it null?

You've loaded an element which is already the <settings> element - that element doesn't have any <settings> descendants. (Descendants isn't returning you null, by the way - it's returning you an empty sequence. There's a big difference.)
If you change it to
XDocument doc = XDocument.Load("...");
then it should be okay - or just load it as an XElement and find the <prospect> descendants, given that you've only got one <settings> element anyway...

How to grab children from xml file as a string

I am looking for an occurance of a certain tag in my xml file. If i find an occurance then i want to get its immediate children tags (not their child tags)
Is this possible? If so what do i need to look in to ?
Thanks
<Footballer>
<Player>
<Number />
<Team>
<Division />
<Position />
</Team>
<Country />
<Birthdate />
</Player>
</Footballer>
if player was the input for example then the tags Number, Team, Country Birthdate would be returned

You can try to use linq to xml:
var doc = XDocument.Load(xmlFilePath);
List<string> urlList = doc.Descendants("yourparent");
.Select(x => insert value you want to select).ToList();

Inserting and saving xml using Linq to XML

If i have an XML file settings.xml like below
<Root>
<First>
</First>
</Root>
I Load the XML first using XDocument settings = XDocument.Load("settings.xml")
How should I insert a XML node inside the node First and save it using LINQ-to-XML?

First you need to find the First element. Then you can add other elements and attributes to it.
There are more than one way to find an element in the xml: Elements, Descendants, XPathSelectElement, etc.
var firstElement = settings.Descendants("First").Single();
firstElement.Add(new XElement("NewElement"));
settings.Save(fileName);
// or
var newXml = settings.ToString();
Output:
<Root>
<First>
<NewElement />
</First>
</Root>
Or element with attribute:
firstElement.Add(
new XElement("NewElement", new XAttribute("NewAttribute", "TestValue")));
Output:
<Root>
<First>
<NewElement NewAttribute="TestValue" />
</First>
</Root>
[Edit] The answer to the bonus question. What to do if the first element does not exist and I want to create it:
var root = settings.Element("Root");
var firstElement = root.Element("First");
if (firstElement == null)
{
firstElement = new XElement("First");
root.Add(firstElement);
}
firstElement.Add(new XElement("NewElement"));