I earned the first two limit breaks in Clouds Level 1 set, but now that I've set his limit to Blade Beam, can I never use Braver or Cross Slash again? Is it like that for every level up in limit breaks??
Yes all the case except for Tifa's who are designed that way. Every level but 4 if i'm remembering right has 2 limit breaks in them and you can only use the limit breaks in the level. So once you set someone to level two unless you change them back to level one, they can't use the previous ones. Again Tifa is the exception since her are the slot reels and progressive in nature.
sapp, once you level up a limit break and you set it to the next level, you can no longer use the previous limit breaks. If you want to use other limit breakers, however, what you do is you set the limit break level back to desired level.
So once you level up and change the level of the limit break - you can only use that level.
If you want to use another set of limit breaks you will have to set the limit break level to your desired level.
This can always be changed, but you're limited to use only the limit breaks in that level tier. Like others have said, Tifa's limit break is an exception. Due to working with slots you only miss a limit break on her end if you have multiple misses in that limit break slot. (If I remember correctly, hitting Hit! Miss and Yeah! also makes you skip that limit break).