When can sea units support land battles, and vice versa?
I'm only familiar with the 2nd Edition, but I believe it's similar. (This question doesn't list include support in it's list of differences.)

When thinking about support, it doesn't matter where you're attacking from. The battle takes place in the region troops enter to attack, and only units (ships or land units) bordering the defending region can offer support to either side.

This makes sense: you can't march your troops to the border and yell taunts until the defenders come to you, you have to go to them. Hence attacks are initiated by a March order. It doesn't matter at all what regions border the region your attackers came from. Only the regions bordering the one region where combat occurs--the region being attacked--can offer support to the combat.

Regarding your last point, land units can never support a naval battle. They can't swim well enough.

I bet this was a common confusion from the 1st Edition; the 2nd Edition rules seemed to really drive both of these points home.