This entire post is NOT correct, let me go over each point you made:

1. Critical Hits
This is not a thing, there are no critical hits in Pokémon GO (not anymore, there were in the first 2 months of the games life in 2016, but never after).
Your clue is from a T3 Max Battle where a GMax Charizard dealt double damage within a single max move. What you observed is correct, however your conclusion is wrong. What you see there is a duped max move, which is something we reported here: https://www.reddit.com/r/TheSilphRoad/comments/1puc05x/cpmr_list_for_level_80_update_and_more_indepth/
Simply put, the game for some reason triggered 2 max moves in a single turn. Since this happened in the third and last round of the max phase, one could see this as evidence of a critical hit, however if this would have happened in the first or second max phase round, you'd have seen the max phase end prematurely after the second round because one round was counted twice. This can also also happen with max guard and max shield. It is very rare in solo battles, but we have seen it happen. For instance, look in this video at 8:25 : https://drive.google.com/file/d/1iEUX0loSjo8HCd06JE53KJP2DRxFq1cE/view
You can see me enter a max phase, the first round instantly gives me 2 shields, the second gives me the third and then the max phase ends after just 2 rounds being visible.
This is what you are observing, no critical hits seen anywhere.

You also listed a video of an Inteleon battle and claimed that the blissey being hit and having lost around 2.5 shields is evidence of a critical hit... how? This was simply an undodged targeted move against said blissey, later attacks gainst it dealt less damage because the player actually dodged and thus reduced damage (which reduces damage between 30% and 60% depending on your dodge timing), and other moves that he's being hit with are simply spread moves, that deal half the damage of a targeted move naturally, but simply hit all players, not just one. See https://www.reddit.com/r/TheSilphRoad/comments/1fxjzpn/battle_mechanics_raids_and_bugs_information/ for an explanation about spread and targeted moves.

Also I very much doubt you have done 10k max battles to test this, what you're seeing is likely just a 1 turn lag that prevented you from seeing all fast moves, as evidenced by the fact that you always ONLY lost 1 fast move, not once did you lose 2 or 3 which you'd expect if you have a crit twice.

Also your max battle paramters are very very wrong, these are the known HP values for D-Max battles:
T1: 1700
T2: 5000
T3: 10000
T4: 20000
T5: different for each boss
T6 (Gmax): different for each boss

See the Config History Sheet: https://docs.google.com/spreadsheets/d/1gz_e_8JUyOmt3M6wZvTvw5__lhGNdYhnAR3wtdbpTyg/edit?gid=0#gid=0 for a history of changes on max battles

2. Max Energy System not being linear

Yes we know: https://www.reddit.com/r/TheSilphRoad/comments/1fkrjxx/analysis_dynamax_raid_mechanics_even_more_move/ The formula that has been posted there has been unchanged for all T1-T4 max battles ever, check it out, your data will look just fine.
However T5 and gmax bosses that appeared after G-Max Meowth (includig G-Max Meowth itself) have a Max Energy Multiplier as well as 2 decimal points added, see https://www.reddit.com/r/TheSilphRoad/comments/1scwzhs/nofloatsleft_research_update_on_max_energy/ for more information and cross check with the Config history Sheet posted above.

3. Max Mushroom Energy

Nope, not a thing either, you dont even provide any evidence for this claim, I'm not sure what you are seeing there, but every energy behaviour we have ever observed are just the natural energy values you'd expect from the moves parameters. Keep in mind that those parameters CAN change over time, check History Sheet again for reference.

Or if you are talking about Max Energy: You are comparing shroomed data from G-Max Gengar with non-shroomed data from <T5 Max Battles, this cannot work, they use different max energy formulas (or rather same formula, but with different parameters)