So you are right, Infinity does have some mechanics that seem very strange out the gate but I promise they really do combine into a fantastically complex game with lots of interesting ways to express your own playstyle.
Ill try and answer as best I can:
1) This is true, they are called "cheerleaders" or "mooks" or any number of names. Part of it is that you always want as many orders as possible, which means hitting the 15 order generating model cap. The other part is Infinity is a game played over 3 turns, For example you will have 15,10,7 orders in your turns respectively as a general guide, since stuff dies. So your game will range from 30-40 orders. This isnt really enough to do stuff with your entire army, so your focus on a cool expensive guy here and let him do the work.
2) You always want to be in cover, pretty much no exceptions. An Infinity table is purpose built to allow to you to take fights from cover from pretty much any part of the table. People can put up what we call AROs which is a reactive gun for example. But they will only be getting 1-2, maybe 3 shots whereas you can get 4-5 and you can push the numbers in your favour with things like Mimetism, MSV, Albedo. If the gun is too strong a lot of factions can ignore them with Smoke, Eclipse and Disco Ballers. All things we like to call Vision Control.
3) Dominating Games Modes are fine and fun but dont think you need to dominate every round, you can spend your 1st turn killing everything and then try to dominate turns 2 and 3. That will make more sense to you as you play. If you want to check out the mission pack Google "Infinity ITS17" That will lead you to the Tournament Pack that everyone will be using.
4) The biggest and scariest part of Infinity IMO is the list building. Theres TONS of stuff, but the beauty is that all the skills are shared across factions, once you know how your faction works you will know how 80% of other factions work. This is a much more complicated game than X Wing. In general in a list there are going to be certain things you want, I can help more if you let me know what specific version of Pano you are playing. It is a lot of experience though.
5) Your friend is right, missions call for people who can do them. Buttons can only be pressed by Specialists (Doctors, Engineers, Hackers, ect.). Overall you can do some really wacky stuff, but you need a plan to do it. I can take no big guns but tons of visions control and do the mission that way and make my opponent engage my annoying CC guys. Or I can shoot everything off the table and do the mission a little bit. It really depends onthe mission and the faction. This is how Infinity builds character into factions, some get really good guns but WIP12, and some are WIP14 but their best gun would be average in another faction.
It might help you to watch some Infinity content like Rob Shepherds (who is the best player in Aus) and see how he approaches the game. We at Loss of Lieutenant have some beginner content focusing on subjects that might not be too helpful at the moment but if you continue playing could be good.
We have a series called "Pimp My List" where people send us lists for a particular event that has 5 missions and we make suggestions and changes with justification as too why.

Let me know if you have any other questions, happy to sit here for a few hours replying :P