Sites such as
https://bitcoinfees.21.co/ calculate the average fee value required for approval of transactions.
The higher the Fee value, the sooner we are approved. Does this have a certain limit? If the value of the Fee is too high, is it possible to be approved in less than 10 minutes?
No, it can not be "approved" (confirmed) before the next block. A high fee will just make it likely to be included in the next block, and on average it takes roughly 5 minutes for the next block to appear.