sounds like you had fun
But not to stray too far from the topic, questions.
How exactly does activation of mechs work when there is uneven number? We looked over the table in the AGOC booklet but we really couldn't understand it.
you're working toward an even ratio - 2:1, 3:1, 4:1, etc and keep moving one unit each until you've reached that ratio. so if for example you have 5 units and your opponent has 3, you each move one and that gives you 4 left vs 2 left. now you have a 2:1 ratio so the person with 4 units moves two at a time vs the person with 2 that moves one.
Second is thoughts on tinkering with the record sheet mechs. Like if you wanted to remove Machine Guns and it's ammo from a Battlemaster :) Is this generally a cool thing to do? Or are such modifications frowned on by players or storywise in the Battletech universe?
there is a full set of customization rules for in-universe tinkering as what you describe. for your purposes, you can just edit the mechs. due to a large volume of munchkins back in the day (like 1991), a lot of players are twitchy about allowing customs for fear of getting a bunch of optimized min/max machines (emotional scars heal very slowly). but if you want to try it out, go for it!
Additional question about crits. Say you get hit in the arm and it destroys all the internal points and the additional points are transferred to the adjacent torso which also goes internal. Do you roll a crit chance for both the arm and the torso in this case? Or just one? Does the arm crit transfer if there are no locations to destroy in the arm?
you roll for a crit in both locations, though if there are no explosive components in the arm, you can just skip it because you're losing the arm anyway. If the arm's actuators have all been previously blown out, then yes, the potential crit will transfer to the torso.
Then a couple of line of sight dilemmas. A mech is in depth 1 water does it have a line of sight to a mech that is behind a level 1 hill?
yes
Then if a mech is standing on a level 2 hill with a level 3 hill between that and a mech that is out in the open some 6 hexes away on level 0 with at least 1 hex away from any hills, do both mechs get partial cover against each other?
the mech on the level 2 gets partial cover. mechs never get partial cover when like Anakin Skywalker, occupy the low ground.
What happens if there are two level 3 hills between them, does it change anything?
nope. only a level 4 hill or taller blocks LoS in this case or if the low-ground mech is adjacent to a lv2+ hill
A mech stands on a level 1 hill, there are two light forests between it and another mech (all on level 0) does the light forests do anything as they cover only half of the mech?
no benefit as the mech is considered at level 3 and the forest at level 2. as forests do not provide partial cover, there is no defensive bonus. there might be something in the optional advanced rules about leg hits potentially hitting the forest but i don't know those.