Character creation

Oh, yeah, I'd imagine they are pretty situational and for you to tell us when/if we need them. But there are some that are awarded by feats, and they should be on the sheet, yes? And the penalties for lack of training, etc.

Penalty for lack of training is actually considered a Skill Rank Die; you have a -1d8 because you have 0 ranks. Most feats should list their bonus as a Skill Bonus; a Skill Bonus should always apply, but bonuses that are conditional are General Bonuses. I'll be reviewing the feats and perks to make sure this is true.

Let's take Talented as an example, it says:
That +2 skill bonus won't be a +2 to the skill rank, but a 1d4 bonus die. So if I take that bonus for a skill I have no ranks in, I'd have a -1d8+1d4, because I may be talented, but haven't put the work to improve. Am I understanding it correctly?

And if yes then the bonus would need its own column. Not the penalty, because it goes in the "skill die" column, just with a minus.

You've got it! This is a great example of when someone says "Kid, you've got talent, but you lack discipline,"

Does this
take precedence over this
?

As in, can I have Tool Training in skills that don't have enough ranks? Like if my occupation gives me 5 tools, but their corresponding skill is just at rank 3?

A rank in a skill grants you Tool Training and/or a Specialization. However, Tool Training and Specializations aren't tied to any one skill, not necessarily anyways.

I am asking about specifically starting Tool Trainings and their max number.

For example, a new character has Int modifier of 2, 5 ranks in Mechanics and 5 ranks in Artistry. Do they have 8 Tool Trainings (Int+6), 10 (as per ranks) or 18 (added together)? (Ignoring Specializations, I'm only interested in Tool Training limit here.)

18.

And there's no limit, no ceiling. You can have lots of Training. In fact, you likely will.