Regarding stat caps to STR/DEX/INT, there is no known cap. It is likely SE has done away with caps in favor of capping out stats using item level. At present, you literally cannot have too much STR, DEX, DET, Crit, etc. Also, DEX no longer affects accuracy.

Regarding ACC, you will hit 95% of the time if your level is equal to your target's level. You will need 1-2 pieces of level-relevant ACC gear to reach 99.99% or 100% against a target of equal level. This is true all the way up until Bahamut's Coil, where the demands of ACC are much higher.