1. How do you capture living alians?
First, do an autopsy so you understand more of their physiology. That'll open up more research so you can build a stun rod -- that'll do for a start, although it's bulky and melee-only.
Oh, and you'll need a place to put them, and equipment to keep them alive.
2. How do you capture ufos?
On occasion you'll get a mission to deal with a landed UFO. Kill the aliens, take the ship. If you shot down the UFO yourself, it'll likely be too damaged to use except for parts.
Regarding damage, don't worry about damaging the ship *during* the fight. Doesn't happen, AFAICT -- so bring the grenade launcher.
*snip*
5. How to I increase credits (money)? As I play the game, the credits go lower and lower.
Sponsor nations pay you at the end of each month. Keep 'em happy -- i.e. do missions promptly and save the civvies. And yes, the loot can be sold as well if you need the money or space.
6. How do I shoot ufos? That is either from attack ships or from missile bases?
Interceptors will need sufficient range, plus an equipped weapon w/ appropriate ammo. A missile battery building requires an installed AA51 launcher (does not come included), and there must be AA missiles (ditto) in the inventory... and the range is fairly short, too. Click the UFO, select the interceptor or base to get the latter to target the former.