1. No STR damage:
The wielder applies his Strength modifier to damage dealt by thrown weapons (except for splash weapons).
I wish that line also appeared in other useful places like the combat chapter, to make it easier to find, but there it is.
2. No extra damage on large creatures:
If the target is Large or larger, you choose one of its squares and the splash damage affects creatures within 5 feet of that square.
Note that it says you chose ONE of the large creature's squares and the splash damage affects CREATURES (not squares) within 5' of that square. So each creature in the area takes damage only once.