The thread is good here: a little TO content in your post aside, this forum covers base rules such as this, which are included in the BMM.
All terrain modifiers apply to physical attacks, including the partial cover modifier when appropriate. Partial cover also eliminates leg hits in this case, as per usual. However, any physical attack against a mech in Depth 1 water that rolls on the punch table does not receive this modifier, because that attack cannot hit the legs. So page 26 is accurate. The partial cover mod would still be relevant vs things like standard hatchet or sword attacks, club attacks, and charges, all of which roll on the standard Hit Location Table.
Page 35: The first para is the issue. For (literal) kicks, consider a target mech in Depth 1 water.
If you're in Depth 2+ water, you can't kick the target.
If you're in Depth 1 water, then it's a standard kick, though the partial cover modifier applies.
If you're in level 0, then you use the punch table, and so no partial cover.
And yes, the para implies that punches receive the penalty, and they don't. The section needs to be rewritten; thanks for bringing it to my attention. Corrected p. 35 Partial Cover text (replace both paras):
Partial Cover: For a standing biped ’Mech, Depth 1 water provides partial cover against any physical attack that does not roll on the Punch Location Table (bearing in mind that the attacker and target being at different levels can change what location table an attack uses; see the Different Levels Table on p. 34). For a standing quad ’Mech, Depth 1 water always provides partial cover.
If partial cover applies and the attacker is at the same LOS level (see p. 22) as the target, a hit that does not use the Kick Location Table and resolves to the legs is ignored; charges ignore this rule.
Does that clarify things? If not, please let me know what part still confuses you, so that I can refine it further.
As for Tactical Operations, the BMM is written so that it ignores other books, because it was designed to be self-contained. But the partial cover bonus would apply against grappling and grabbing attacks, while tripping attacks would be impossible (because the legs are protected) unless the attacker itself is in Depth 1 water.