If the tile is placed onto an existing water tile, does the emblem determine how the tile is rotated upon placement?

Yes.

When a beach is completed, must the convoy of boats leave from only that beach or can it be from any beach on the island?

Only from the completed beach.

In fact the rules state that:

1. If more than one beach is full you must state BEFORE turning up a tile from which beach you will be leaving.

AND

2. If a beach has more than one wooden footbridge (jetty) you must state BEFORE turning up a tile from which wooden footbridge (jetty) you will be leaving.

After turning over the first tile the red emblem is placed opposite the chosen wooden footbridge (jetty). Subsequent sea tiles must be placed with the red emblem opposite the end of the sea route along which you are moving.

I hope this is clear.

I've just played my first game of Tongiaki, before reading this forum and now I'm confused.
Where does it state in the rules that you place a water tile on top of another tile ? Surely new tiles always build out from the end of a 'path', not overlay them ?

Right. The original poster meant to say "adjacent to" or "connected to", not "onto".