The biggest thing that's blocking you is no access to Alien Vocabulary. For that, you need Alien Wave-Field Theory. This can be beaten out of a whole array of different alien engineers and leader types. Sectoids, Floaters and Mutons all work.
Then you need Grav Shield, and for that you need Tractor Beam Generator. This can again be had from the same engineers and leaders, but requires Alien Vocabulary.
Same deal with Grav Module Construction and Alien Gravity Generator.
Finally, you need Anti-Matter Containment. Same as above, but no post-interrogation topic between this and the Advanced Laboratory.
As to capturing aliens, Sectoids go down pretty easily once you get rid of their shields. Floaters are not terribly tough, either.
I've had some good experiences with Stun Spears. You don't seem to have them for some reason.
Taser Cannons are pretty good because they're somewhat armor-piercing. Not much else that agent is going to be doing, though.
There is also no need to use 'pure' stun. Beat them up and then perform the final blow with a stun weapon.
You have Psi-Amps, so going for a few psi-captures towards the end of the mission can work. Not sure what you did with your hybrid defector, though. Wait, you don't have that, either. Your capture&interrogate game could use some improvement. There's a whole bunch of stuff you actually have not researched because of that.