Do the points you stick into the areas to help improve you (Eng,Sci,Ass) awayteam crew also improve your skills if you are that class?

If you mean the 'Team Leader' skills in the Starfleet Training group, they have two effects that I know of:

* They boost the ground abilities of bridge officers of the appropriate class
* They boost the appropriate 'Team' space ability (Science Team, Engineering Team, etc)

I don't believe they have any effect on your captain's ground abilities - those are boosted by your skills in the Tactical/Engineering/Science Officer skill group (depending on your captain's class).

Yep. If you plan to use BO's of a given type, you should max the appropriate skill, and the "Team" skills are all very good as well.

Could one of you kind souls help me understand the 'Team' space ability part of this. thanks

Some bridge officers have "[Class] Team" powers: Tactical Team, Engineering Team, Science Team. These are self-or-ally-targeted powers (you can use them on yourself or any ally) that provide temporary boosts to certain things.
Tactical Team helps repel boarding parties and boosts damage (I think).
Engineering Team boosts hull repair rate and damage resistance.
Science Team boosts shield strength and something else.

By increasing your Team Leader skill in the appropriate area, you increase the effectiveness of these powers since adding skill points to your bridge officer for that skill only reduces the cooldown.

Thanks to all who posted. You help me tons. See you all ingame.