Welcome to the forum,
900ssduke. Traction control stays on in low-range, but can be disabled together with VSC. LSD is useless for the serious off-road stuff, even when shimmed (mine is also an Invincible and I've been down that road). And no, Invincible doesn't come with rear locker, have to go with either Active or Icon pack for factory locker or you might consider aftermarket locker. Although it might be overkill for what you're gonna use it for.
Now, tell us a bit more about yourself in the Introduction section, so we can give you a proper welcome