First of all yes if you flash any different rom you will lose warranty. But there are ways like rooting first then claim warranty back via TriangleAway and then flash Oficial ROM's via paid version of MobileOdin. You can find how to do them in this thread.
For your second problem, Your phones cable connector can be malfunctioning via bending or liquid contact. Check with another data cable for confirm if new cable doesn't solve problem contact to service in your region. Your data cable/recharger adapter could be broken if changing data cable/recharger has solved your problem you need to replace data cable/recharger. And there is a slight possibility that your android system has gone haywire and cannot determine how much battery left. You should make a complete wipe cache/fatory reset then empty your battery fully then recharge it to %100 capasity. If this gig doesn't work for you should contact to service in your region. What you told is impossible for new device.. I have mine about 2.5 months ago and still it goes about 2-3 days stand-by and 20-22 hours of on screen note taking..
Your third problem looks like you are using battery saving apps like JuiceDefender.. If you are using them it's normal for them to block mobile data for squeeze as much battery life as possible. There are variety on these programs so every program has own solution for it. You should look for them in those app's pages or help menus.
If you are not using any kind of battery saving / battery life extending app then you should go to service and hand over your phone for repair. It is most likely a hardware problem..
If you stuck with anything you can ask here again, we will try to help you as we can..
You are on very wrong page..
What you are asking us to do is like future reading..
You should go to development pages and follow favourite ROM's threads for this kind of insights.. There is developers and experienced ROM users talking, suggesting and exchanging opinions about custom ROMs future.. I don't know is anyone here follows them but i don't.. I'm merely trying to help with lots of questions/problems and no idea how to get help, where to look, what to do, etc..