Any way to check the price of BNB that the bot is using to convert Hive to BNB?

Currently, no. The best way is to check HIVE and BNB price and do the calculation yourself. Soon though.

Also is there any bot to convert Leo to Cub?
Or if you are aware of any best way(economical & fast way) to do it.

No bots, unfortunately, you have to convert LEO to Hive and then Hive to BNB and then buy CUB that way.