When I try to mine cobble or ores, dig dirt, etc. the block will pop back up a second after I have already mined it and I will have to mine it again. bug or just extreme lag?
It might, but it's unlikely. This happens after the server has been up for awhile, there are too many entities in the mining world, or a variety of other things.
Just to let you know fast break is not allowed because anti cheat blocks fastbreak and makes you break a block 3-4 times with fast break on just like the problem you have.