How do I find out if a remote system is still alive, if certain services are running, which processes are running, etc.?
You can use ping to see if the system is alive:
ping -c4 <system's IP address>
To see if a certain service is still alive, use the telnet command:
telnet <system's IP address> 25 (for SMTP)
telnet <system's IP address> 80 (for HTTP)
telnet <system's IP address> 110 (for POP3)
You can login to the system using SSH (port 22) (use PuTTY if you are on a Windows PC; PuTTY is an SSH client for Windows), and when you are on the system, you have a few useful tools to gather more information:
uptime (shows how long the system has been up)
ps aux (shows a list with all running processes)
netstat -tap (shows a list of all services that are listening on some port)
top (shows the system load)
dmesg (shows bootup messages of the last boot)
You can also have a look into the log files in /var/log/ to find out about errors, etc.