As far as weight goes:
Openxcom by itself doesn't change any of the weight rules, they're the same as vanilla. OXC in general doesn't change vanilla rules except when neccesary, and certain things, like removing the 80 item limit for craft, are optional. There's an option in the settings (pretty sure it's in base OXC, but might be OXCE) to put make certain stats visible in the inventory, including weight.
As for encumbrance:
Encumbrance = Strength / Carried Weight*
If Encumbrance >= 1 then
Available TUs = Base TUs
Else
Available TUs = INT(Encumbrance x Base TUs)
https://www.ufopaedia.org/index.php?title=Time_Units#EncumbranceAs far as I know, no OXC/OXCE mod messes with this. Overloading your units gives them a penalty based on how much they're overloaded, and it's multiplicative, meaning it'll be worse for low strength soldiers and more bearable for high strength ones. A 20 Strength rookie, for example, carrying 25 weight worth of equipment will have a 0.8 encumbrance multiplier, while a 70 strength superhuman carrying 75 weight will have a 0.9333 etc. multiplier. This means that the rookie will lose a full 20% of his TUs, while the Superhuman will have a much less punishing loss of roughly 7%
This is separate from direct stat modifiers, which (to my knowledge) can only come from armor and (OXCE exclusive) transformations. Armor will modify the base stat in the above formula. Thus, if you have a unit with 65 base TU, and an armor that removes 5, his new base TU is 60, and that new number will be used in the formula if he carries more than his strength limit.
Some mods also have armors that effectively reduce strength by taking up weight points themselves. Eg. my soldiers are currently using an armor that weighs 6, so even if that unit has an empty inventory, he still has 6 weight taken up. This is usually a way to balance armors. Those 6 weight points prevent my soldiers from carrying say, two extra grenades, or a magazine for their cannon, but the armor is highly protective and that's arguably worth more than the firepower.
Regarding weapons and TUs:
You are correct in assuming that the % refers to the base TUs before encumbrance. Returning to that rookie from earlier, if he's carrying a weapon that requires 85% TUs for an aimed shot and he's overladen such that he only starts with 80% of his TUs, the only way he would be able to shoot is if someone gave him extra TUs (don't think there's anything like that in Vanilla, but some mods have such items), or if he dropped whatever was overloading him and waited til next turn.
Also remember that armor modifiers apply before the battlescape, while encumbrance applies
on the battlescape. So regardless of how many TUs an armor takes away, the % will be based off the base TUs which were determined before the battle started. You could have a suit of armor that reduced a soldier's TUs down to 4, and the 75% attack would then cost 3 TUs, regardless of the soldier's stats before armor. Thus, no matter how many TUs a unit has, they will always be able to make the same number of attacks with a given weapon. TU growth is mostly useful for movement.
Not sure on terror AI, but I do know that some mods have more dangerous AI routines.