'at sea' and 'at the sea' is the same I guess. But I would use 'at the sea' when the 'sea' was mentioned previously. And 'at sea' with the word 'out' infront
e.g.: I am at the sea now.
I am out at sea.
(Not too sure, sorry!)
'On the sea' would mean something is on it :
-A ball is floating on the sea
- There is a boat on the sea
'In the sea' can mean inside the sea itself:
- There are many fishes in the sea
or it could mean the AREA the sea is:
'There are many boats in the sea'
1. I would say "In" is the right one because you are talking about something happening IN Boracay.
2. kite-surfing on the sea.
(Basically, you are on the sea, not inside under the water)
3. Correct
4. 'At the beach' would mean you are at that place, whichever parts of the beach, you are at that AREA. ("on the beach" is not wrong but "at the beach" is more preferred to "on the beach" to me)
Not the best answers but I hoped it helped!
^^