First of all, what version do you play? Is it 2.2.1 release or on of the current dev versions? Also, What difficulty level are you playing?
1. How do you arm your interceptor? I usually mount 2 sparrowhawk missile launchers and a tr-20 missile pod,, + armour and one of both ecm and targetting computer, and on standard difficulty settings this usually does the job. If it doesn't then try to send two inerceptors and back them up with a missile launcher from the ground (build a missile battery in your base). you can also try to lure ufos over your base with the firebird dropship (but that may take some time to learn)
2. How many workers do you have in your workshops? If you have one worker even a construction of a sniper rifle mag will take (afair) 1200h. Production times are displayed on the panel on the right. If production times don't satisfy you, construct another workshop and hire more workers.
3. funding from nations is displayed in statistics, in 2.2.1 it's one of the tabs on the lower left window, in 2.3 it is on the panel on the right.
4. to capture a live alien perform any autopsy AND research the alien breathing apparatus. That enables researching of stun rod, meele weapon used to stun and capture live aliens. There is another way, but that is up to you to discover.
hope this helps