Just curious....did you buy this new, used, what?

Check your PMs. 

I have no experience, but I have a son that games. I don't think you have to be online.

Question 1, If you have an X-box Live Gold account, it will keep track of that info for you, as long as you are signed in under your profile while gaming.

Question 2, No. You can game with the unit off line and without an active X-Box Live Gold account but you will not be able to multiplay or enjoy the benifits that an X-Box Live Gold account adds.

Normally Best Buy has sales around Christmas for a years worth of X-Box Live Gold for around 50% off. You may want to pay mothly untill you can catch it on sale if you want to check it out. At $25.00 a year, it's definatly worth it. Without a Gold account, you can't access Netflicks, Crackle, HBO Go, or any of the other cool features.

Check out the features of a gold account here.

One thing to note, if the previous owner of the X-Box 360 had his machine banned, you may not be able to use an X-Box Live Gold account on it.

All we signed up for was a free account. We have no desire to use any of the apps or play games with others over the network.

I will say this. The Xbox menu layout sucks. Why can't it just be as simple as the PlayStation menu layout? To many things in the menu use the internet connection. Kinda overkill. And this whole pay-to-use Xbox Live stuff? Why? PSN is free.

Those are the sorts of things to consider before purchasing a gaming system.

 Just sayin'

You assume I purchased the system. I didn't. I just use it. I'm more of a PlayStation type of guy.