To retrieve the database node based on its name:
XElement PDMDataBaseName = xml
.Descendants("Settings")
.Elements("DataBase")
.FirstOrDefault(el => (string)el.Attribute("Name") == "PDMDataBaseName");
To retrieve the file paths:
IEnumerable<string> filePaths = xml
.Descendants("Settings")
.Elements("FilePath")
.Where(el => (string)el.Attribute("Name") == "FileDirectories")
.Elements("Path")
.Select(el => (string)el);