How does Potency factor into the damage formula

You will occasionally receive a stat point when you level up, starting at level 10. At level 50, you will have 30 total bonus points to assign. This amount is always the same for each class that you level, regardless of your class, race and god choices.

You get separate stat points for each class you level up, and assign them to your attributes for that class. So you can put everything in Strength as a Pugilist, then change to a Marauder and put everything in Vitality. When you change to a job associated with that class (ex: Monk for Pugilist, Warrior for Marauder) those stat point allocations carry over, and cannot be changed separately from the base class. This normally isn't a problem, but causes a slight complication for Arcanists since its two jobs, Summoner and Scholar, use two different primary stats (INT and MND, respectively).

If you don't like your stat distribution for a class, you can reset it (freeing all the stat points you've used on that class) by using a Keeper's Hymn, which you can purchase from your Grand Company for 10,000 seals.

No to combat. It would be certainly neat if it did though.

Partial Yes to spawns now, some special mobs only appear during certain weather conditions (iirc, its only Odin and his lightning weather atm, but I seem to remember something requiring the gloom weather).

It does also affect fishing, even more so with the highend fish (stupid raincaller), and greatly so with the recently added "Big Fish." The Sightseeing Log also usually requires that you visit each vista during a specific type of weather and time-of-day.

The 2.35 update (Aug 19, 2014) added "Skywatcher" NPCs that will give you an in-game weather forecast for the next 8, 16, and 24 hours (Eorzea time).