Waterfall or Dragon Tail on Milotic

Personally, I would go with dragon tail over waterfall. You're doing a bit less neutral DPS in exchange for slightly better EPS. Plus, DT will (in my opinion) be more relevant due to the presence of dragons in both the great and ultra tiers. If you're looking for a water specialist, Blastoise has been my personal favorite.

As for Tyranitar, fire blast can function as a nice backup option as a second charge move, but if your t-tar only has one charge move, I would TM it to either stone edge or crunch.

For PvP:

1) Depends on what you're using it for. The product of Damage per Turn and Energy per Turn (one good measure of the power of a fast attack) is 10.00 for Dragon Tail (no STAB) and 10.67 for Waterfall (STAB). Dragon Tail generates energy a little faster (3.333/Turn vs. 2.667/Turn), but Waterfall does more damage (4.00/Turn vs. 3.666/Turn). Of course, if either has SE or NE damage for your foe of choice, that takes priority over these numbers. Hence, it depends. But they are pretty close.

2) Fire Blast on TTar is a surprise to use against Ice, Grass, and Steel. Of course, TTar is weak to Grass and Steel, so all it does there is level the playing field, in that whoever hits with a charged attack first wins. With Bite (low energy generation) that's usually not TTar. (Ice is just as weak to Stone Edge as Fire Blast - but even with STAB, Stone Edge does a bit less base damage (power) than Fire Blast).

So, in general, I'd say very little use. If you're going to buy a second move, do so, and then TM Fire Blast to either Stone Edge or Crunch.

For PvE (Raids and Gyms):
1) Waterfall for offense. STAB is good, and you use it against stuff weak to water. As a Gym Defender, Dragon Tail gives better coverage, especially to Grass.

2) No. Just no.

I have a milotic with dragon tail and blizzard. I recommed it strongly to face the dragons it works a charm and sinks them.

Also just TM your ttar! ideally you get crunch on it but stone edge is pretty good especially if you have the legacy on it, also super effective against flying types and it has stab :)