This question is less for me and more for my players. Do they use "Increase a skill value of 12+ by 1" or is it mostly reliant on schticks to increase? Thank you for your time.
Increase skill value 12+ by 1 to raise the main attack but you cant raise a stat if its already the highest in the game per your fortune stat type, i.e." Sam has the highest martial arts AV between the 2 players with chi so he can no longer raise his martial arts until the other player ties his martial arts AV also Sara in the same game is the only player with the standard fortune stat type so she has no limit to what she can raise her stats."
I'm afraid that's not Rules As Written (though of course you can houserule all you like!) - as per p25 of the book, you only increase a Stat (i.e. one of Main Attack, Defence, Toughness, Fortune/Chi/Magic/Genome, or Speed) by 1 on advancements that are a multiple of 5. So on your 5th, 10th, 15th, etc ...
The restriction about not being able to increase a Stat if it's already the highest in the group does apply, though.
(You can't go hog-wild if you're the only one in your group with that Fortune type - that only applies to the Fortune stat, your other stats are still limited until the others catch up if you're out in front.)
(You can choose to delay that Stat Advance, and pick a standard advance for your 5th and take the postponed Stat Advance for your 6th, or 7th, etc., instead)
All other advancements are taken from your archetype's advance list (so, new Skills, improved Skills, new Schticks, or increases to your secondary attack, as relevant). Skills (e.g. Detective) are not the same as Stats, and the "Increase a Skill value of 12+ by 1" only applies to SKills.