Centaur Race Build

This product is very well presented, especially the art, but I have a few concerns about the mechanics:

1. For clarification does the "trample" ability use an action or does it occur as a part of movement? If the former, making an attack roll would make more sense to me, and if the latter, that seems quite strong but still something you could build a race around with some adjustment, especially if it becomes the primary combat-related benefit.
2. I would suggest for balance reasons that instead of gaining +1 to attacks made with certain weapons, that proficiency be given instead. Indeed, I would suggest giving proficiency or advantage in place of flat bonuses to all places in the supplement that do so (besides ability score increases), and the -2 to Charisma isn't really necessary. Also, automatic advantage to saving throws is quite strong. I would recommend changing the wording of the mountain centaur's sure-footed trait to gaining advantage on saving throws against falling. I would...See more also probably reduce the number of skill proficiencies to one per subrace if trample is meant to be a part of movement.
3. As written, arid centaurs have a speed of 0 ft. when in the water or on other non-solid surfaces in exchange for a 70 ft. land speed, which when compared to 60 ft. isn't much of a boon when falling into the water can mean almost certain death.
4. Because there seems to be some uncertainty in the text: there is a difference between between ability checks and saving throws. Saving throws have nothing to do with skills and are usually made against a spell, a creature's special ability, or trap. Ability checks, have to do with things relating to the skills (and tools such as artisans' or thieves' tools). Bonuses to saving throws are more powerful the more general they are. I would follow the example of the dwarf and the elf and give advantage on saves only against specific conditions (such as the dwarf's advantage against poison and the elf's advantage against being charmed). Bonuses to ability checks in the way of proficiency or advantage are less powerful but still solid and are nice flavorful additions to any race.

I do enjoy the art and the flavor-text and hope to be able to see more ideas from you. The idea of a small coastal dwarf-like pony centaur never even crossed my mind before but I love it.