1. Impulse doesn't have an auto-update option for installed products (at present), but if you look on the My Games tab anything that does have an update available is clearly marked with a ( ! ) icon so you can see which ones need updated.
2. Yes, if you have DL/DA/TA installed, and are playing TA, you have all of GC2.
3. Depends on how the mod is designed, if it replaces the base files or uses the mods folder. Really a question for the mod authors.
4. There is a beta version on Impulse for the upcoming TA 2.0 update. Any version numbers of mods are not generally related (in most cases, the mods were first made for DA or earlier, so their 2.0 was for TA's initial release).