There are 2 roms currently that run 4.0.3, I believe. They are still somewhat of a dev stage, but I believe they run peetty well, with some minor issues, of course.
Side note, which extended battery did you get? I personally bought one off ebay that states 3600 mah. Whether or not I actually get that much is doubtful. Here's t hoping though. For 10 bucks though, if i even get a little more than than stock, I'll be happy.
As far as apps go, just go online and find the older versions that are compatible with your os version. Make sure you check allow from unknown sources and read the comments to.make sure they are clean before installing.
Hopes this helps!
sent from that HUGE Phone