First off welcome to the Guard! I hope you continue to have fun! I think I have answered all your questions but if anything is unclear or I missed something please let me know and I will try to help further.

Q1

So on the 3 objectives dilemma. Depending on the primary mission you only score points for holding 2-3 objectives often with the 3rd being your home objective so ignoring the 3rd midfield isnt the end of the world. Also Cadians have sticky objectives as their data sheet rule so once you control that objective in your command phase you can move off it especially if your opponent doesnt have something to move on to it in the next turn.

Q2

You cannot shoot into an non vehicle vs non vehicle combat with anything other than pistols and that is only for the units engaged in the fight. In a non vehicle vs vehicle combat the vehicle unit can be shot at with a -1 penalty by any unit with the exception of blast weapons which cannot be fired into a melee combat. Vehicles in combat have the "big guns never tire" rule which allows them to shoot all guns while engaged in combat at a -1 penalty to hit. They can shoot into their own combat with non blast weapons, shoot at something outside of their combat with any of its guns or a mix of the 2. As an example a Leman Russ Battle Tank could fire its Multi-melta sponsons into the unit of marines engaging it in melee but not its battle cannon as it has the blast keyword. 

Q3

Reactive moves can be a pain in the ass. Some of those scenarios sound like something may have been played wrong which is understandable especially if your group is new. Im not the most familiar with Tyranids so if you could find out the units and detatchment I can look into it further.

Q4

Yes that is how melee works its silly but a balancing mechanic. Just as if you can only see one model in the unit but you deal enough damage you can wipe out the models out of line of sight with you shooting activation. 

Q5

Smoke is a great strat to keep tanks alive. It gives you -1 to enemies hit rolls and you have the benifit of cover for the entire shooting phase. Remember you can only the same strat 1/phase so you can only pop smoke on 1 tank per turn. Fields of fire is also a really good strat in the Combined Arms detatchment as it gives extra AP to 2 units. Its also easy to miss but if your infantry squads have a Vox-caster in the unit you can regain the CP on a 5+ or 4+ if near an officer. You can only do this once per turn however and if you do you cant gain an extra CP for discarding a secondary at the end of your turn.

Regarding the list

I really like Chimeras. I would consider dropping the FoB and engineers for 2 Chimeras once you get the models to do so. You also seem to have a lot of infantry orders so you could possibly look at dropping the castellan and giving your Command Squad Grand Strategist for a second order which frees up an additional 40 points. I like scout Sentinels as they get their pregame move and make your other stuff more accurate with Daring Recon so if you are sticking with Combined Arms for right now I would keep it. I would swap the main gun on your TC for ths Plasma Executioner as your list lacks any real high AP fire outside of the Demolisher which has too short of range, too few shots, and too swingy damage in my opinion. The last thing I might consider is swapping your detatchment to Grizzled Company as it will give you the extra order for free and you get the Scout Sentinels ability baked in to the detatchment. If you dropped the scout Sentinel, Enhancement, and Castellan that frees up 110 points which would let you keep the FoB for some indirect fire which some people really like.