Hi JayOni.

First, ping -a will give you a hostname that an IP resolves to, if the IP is registered in DNS, or a nameservice.  If not, you'll get the same address returned as a result, similar to what you get without the -a.  So, it's useful if you have an IP you're looking at, and want to see what hostname belongs to the address.  Say you review a log, and see an IP regularly hits your firewall.  You might try -a, to see if you can determine the host.  Subsequently, in a test, you might ping sweep a range of addresses, to see which are responding.  You might then try to see what the ones are, that respond to the initial sweep.

Next, -t is handy if you're doing connectivity testing.  For instance, if you suspect you have connection issues, or want to see if there's packet loss, etc, you might run a continuous ping, to see if you are not getting responses to all your ping packets (meaning it either dropped your outbound packets, or the return packets, somewhere.

There are other scenarios where you might use it, but that's one example.

As for stopping it, the combination of ctrl-c essentially stops the running ping process, in it's tracks.  Like 'break'

May you could answer another noobish question, and keep in mind im not looking for a how to guide but more of general understanding.

I've been learning about ports and stuff and know like 15 of the main ports, but i've sorta been wondering how people (mostly hackers i would suppose) gain access threw ports to your computer remotely I know you have to have the port open and they would probably run a port scanner on you or something to see which ones you got going but how do they access it from there (do they use the command prompt or a 3rd party software)?