Yes. As long as you own the Xbox Live Gold Membership, you can play games with friends whenever you want. To physically communicate with them, there are multiple methods. The easiest, of course, is to get an Xbox-made microphone that attaches to your controller/console so you can talk and game together. A simple phone call on speaker works as well. Skype, Teamspeak, and other services provide the same enjoyment to little to no cost. However, if you really want to save tons of time and money, just get a microphone for your Xbox. They sell cheap at less than $5 at your local Five Below and are extremely easy to set up. Without Xbox Live, you can't do anything I just mentioned above via Xbox. Without Xbox Live Gold Membership, you can't talk through Xbox but you still can talk through other sources. I haven't had this problem much but most games won't allow you to play them without a membership.
Chat with our AI personalities
No you do not, you can use xbox live weather you have the headset or not. If you want to couminicate over live then you will need the headset.
Most of the time the Microsoft one only works, but I believe there are some that might work that aren't made by Microsoft.