A314 No. Deadly Aim benefits ranged attacks, while a slam attack is melee (it also specifically benefits from flanking and threatens squares, something ranged attacks don't do naturally).

A315 I believe the RAW answer is "No." From the text of Improved Natural Attack:

Choose one of the creature's natural attack forms...
Compare with the text of Watersinger:

...the water's slam damage...
The water does not use your slam damage, it uses its own slam damage. If the water could somehow gain feats on its own, it could take Improved Natural Attack, but alas, it's just water.

It's not a particularly overpowered combination, so a reasonable DM might allow it, but I believe the RAW answer is that the water makes the attack, not you.

A316 There is no RAW answer as the text of the archetype does not specify either way, but consider the language "the water's slam" and the text of Spiritual Weapon, which has a similar effect. Here's a relevant snippet:

Your feats or combat actions do not affect the weapon.
There are two logical lines of thought:

1. Similar abilities do not allow feats to affect the attack; therefore, feats do not affect Waterstrike.
2. It's not particularly overpowered; therefore, rule of cool, sure, whatever.

I'd like to stress that there does not appear to be a RAW answer in this case, so talk with your DM to find the "correct" answer for your game.