You can play Xbox live using your Xbox360 as long as you have the right game and accessories.
Regarding your game that freezes, what you can do is try to clean the game disc using a soft cloth. Don't use any liquid cleaners to clean it. If that doesn't work, you need to call your ISP to check if you have enough bandwidth. And if all of that doesn't help then its time that you call customer service and let them fix the problem for you.
I hope I was able to help you.

"We can't make all people understand us... We have to accept that having the opportunity to speak doesn't always give us the privilege to be understood..."