I've never seen any algorithms that determine stealing rates, but I have read that at least one item in particular is easier to steal at low Dexterity (for the record, there is not an additional statistic called Agility). Whether or not this is true, I have yet to test myself. In any case, this would not be true all the time, but does suggest a correlation between Steal and Dexterity. Thus, it seems possible that higher dexterity would have some sort of a positive effect on Steal. When you get the Sneak Glove, that obviously increases your chances, but that won't happen for quite some time.

However, initial Dexterity is not so different that one character should have an enormous advantage over another. While it might be easier to steal with another character, it probably won't make a massive difference in your case. Sometimes, it just takes awhile to steal an item.

Mastering the Steal materia has no effect on your rates of thievery; you're already rewarded with a new materia anyway. Using Yuffie, or any other character, has no bonus in and of itself.