Are standings boosts shared to your fleet in missions

I've thought of this myself after realizing that my gallante standing was -7 (running with a Caldari mission corp will get you there pretty fast), and eventually decided to just pump up my social skills. Its quicker then trying to get your standing up, and unless you've completely buggered your standing with a faction you shouldn't be killed on site if you happen to wander into space claimed by a faction that doesn't' like you too much.

The only time I'd worry about having great standing with all four factions is if your character is going super hardcore into industry(and I mean 100% non-stop indy character). If you're in EVE for the pew pew, just keeping your faction standing around the -2/3 area for everyone is good enough to not have your ships popped on sight should say, a war target fly through space that you'd get popped on sight for.

In my corporation, we do missions and somebody loots everything. Then we see if somebody needs anything in particular and the rest gets salvaged. We then either split the salvage, or we give our salvage to our CEO who, in turn, gives us free ships.

This is something you have to make out with your corporation. If they are happy with your system, keep it. If you notice they are not happy with it, ask them what they would change.