You can use XmlDocument and an XPath statement in the SelectSingleNode method to retrieve this information. Here is an example:
XmlDocument doc = new XmlDocument();
doc.LoadXml(xml);
var accept = doc.SelectSingleNode("//string[@name='accept']").InnerText;
var actionSettings = doc.SelectSingleNode("//string[@name='action_settings']").InnerText;
var appName = doc.SelectSingleNode("//string[@name='app_name']").InnerText;
Here is a tutorial on XPath syntax: https://www.w3schools.com/xml/xpath_syntax.asp
UPDATE: @jon-skeet suggested using LINQ. Should you choose to do that, your code might look something like:
var element = XElement.Parse(xml);
var accept = element.Descendants("string").Where(x => x.Attribute("name").Value == "accept").Select(x => x.Value).FirstOrDefault();
var actionSettings = element.Descendants("string").Where(x => x.Attribute("name").Value == "action_settings").Select(x => x.Value).FirstOrDefault();
var appName = element.Descendants("string").Where(x => x.Attribute("name").Value == "app_name").Select(x => x.Value).FirstOrDefault();