Before i get to the individual questions i will mention that the default is that 10% of damage that gets through to hp is applied to armor, some weapons like chem do damage to armor before this step, refered to as either armor stripping, or in game code pre-armor-multi
1) Early game: chem, Late game: Plasma. There are a few other options like RPGs and rockets, but they tend to be a mix between armor damage and penetration rather then one or the other.
2) Mechanically all chem weapons have some, where as pierce is limited to certain weapons. Chem also tends to have a higher % of damage dealt to armor, but less base. Look in the Analysis(Anal) tab for individual weapons for greater details.
3) Lasers ignore 33%, Armor peirce ammo ignores 50%.
4) Fire type damage does bypass armor completely as the default but the behavior is not constant across all weapons that use the type. Check Anal carefully here.
5) No, Laser is %, Fire is highly dependent on weapon used. The nitro gun functions as vanilla fire effects(bypass armor), but doing 50-150% times (5-10) and then applying several more modifiers to that damage.
6)No, general rule is that chainguns style weapons and weapons over 60 base damage have thee stip effect. Again check Anal.
7) Plenty, effective range, accuracy, ect. Check Anal
This is a very complex and fluid answer as there is no one best tool for all situations. It depends highly on what you have access to at any give time and what the actual target is. Foes can have a great difference in what types of damage they resist, is it a 2x2 unit, does it have sheilds as well. I could go very deep into the topic but it would be a wall of text, and probably not make much sense to you at the moment. But feel free post about specific targets for a slightly more digestible answer.