In theory, it's still possible that someone perform a 51% attack.
About %51 attack. If you have hashrate higher then %50 then you can manipulate some part of the blocks.
Take note you can try to perform a 51% attack even with less than 50% of the total hash rate and you will be successful if you are lucky.
Can we put BIP for full nodes to check if the block comes from a %50+hashpower producer and if so if there is anything wrong they reject it. Is it possible or is it being done?
That's not possible.
- As I said, even with less than 50% of the total hash power, a dishonest miner may be able to perform a 51% attack successfully.
- The winning chain is always the one with the most work. If a dishonest miner perform a 51% attack succesfully, their chain would be the winning one and completely valid.
- There is no data in blocks that indicates the hash rate of a specific miner. The hash rate of mining pools you see on some websites are just estimations.
- The mining pools can simply use different addresses for each new block they mine, so that no one can estimate their hash rate.