1) Either you need lockpicks, or they can't be used at all.
2) Grenades are best used indoors, toss one into a room where there's enemies. Their effectiveness outdoors is unreliable. Anti-tank grenades, however, are much more devastating.
3) Yes, it is odd, and doesn't make much sense.
4) Nope, not that I know of. I think the map buttons are purely for decoration.
5) (idk about this quest, and that's 5 questions btw, not 4 )

Edit: Almost forgot, grenades are awesome when you need to catch some fish…