is the block headers are transactions informations (the sender the receiver/time/amount .. etc)
No. The block headers contains the merkel root which contains the transaction hashes which are assembled. They do not contain specific transaction information persay.so the validity of a transaction depends on the Bitcoin Blockchain Algorithm Rules (Mathematically) is this correct ?
Protocol rules: https://en.bitcoin.it/wiki/Protocol_rules.so the pool alse could be called as huge Node, is this correct ?
Pools should be running a node, probably not a reference implementation though. Pools do not have to run a node explicitly, the only thing that they need is the transaction information, previous block hash and all that. These can be easily obtained from various sources.Thanks a million for your help, so helpful thanks a lot again
