You can ping your server by issuing the command ping
followed by the servername or its IP address, like so: ping www.linuxquestions.org
. Press Ctrl+C to quit pinging.
You can set up an FTP server on your computer so you can upload and download files easily. Most distributions come with an FTP server so it should not be hard at all.
As for the mail server I suggest you don't unless you really know what you're doing since it is easy to lax the security one tiny bit and then your computer becomes a spamming relay. If you really want to set up a mail server, implement some means of secure sending - POP authentication before SMTP (sending), or authorized SMTP, or something to that effect.