Other than Battle Armor, can any other infantry type lay mines?
Yes, the rules are in Handbook:House Liao pg 160. At some point they need to be errata'd into TO.
Are the numbers of troopers in the various platoon types found in TacOps generic infantry numbers or do they apply to everyone? For example normal VTOL Micro-Copter Platoon has 4 squads of 4 troopers each, for a total of 16 troopers. Is that for every organization or would a Comstar VTOL Micro-Copter platoon have more troopers?
They are generic. Note that TRO 3085 has platoons that do not adhere strictly to those numbers.
How does Infantry Armor effect how Mechanized Infantry take damage?
The multiplier(or divisor, based on attack type) for mech inf and the divisor(or multiplier in rare cases) for armor both get applied, one after the other. The magic that is mathematics means that if you don't round off until the end, the result will be the same no matter what order you apply these modifiers in. See Tac Ops pg 317
Can Beast Mounted Infantry troopers wear armor?
Yes
Can the animals in Beast Mounted Infantry be armored?
Not specifically. However, the nature of the way infantry platoons(including beast-mounted ones) take damage means that if the infantry are armored, the critters also take less damage.
Can Mechanized and Motorized, tracked and wheeled infantry be made amphibious?
Not under current rules