Yes - you use the System.Diagnostics.Process class. (For a shell
command like dir, I think you'll have to run command.exe, and pass it
a "dir" argument - I haven't tried this.)

Yes.

Here's an example that I wrote (two days ago, fwiw) to capture PING
output:

private static string PingServer()
{
   Process Ping = new Process();
   Ping.StartInfo.UseShellExecute = false;
   Ping.StartInfo.FileName = "ping.exe";
   Ping.StartInfo.Arguments = @"-n 1 -r 9 www.midnightbeach.com";
   Ping.StartInfo.CreateNoWindow = true;
   Ping.StartInfo.RedirectStandardOutput = true;
   Ping.Start();
   return Ping.StandardOutput.ReadToEnd();
}