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What type of data is Ethereum storing (file? data row in DB)?
Where does it put it (theoreticaly it is stored in peers, does this mean every node must have a local db)?
How the peers of the p2p network get the recent copy of the blockchain?
how a peer learn that there is a new block created and need to be mined?
This depends on the client you are using. Geth (most popular Ethereum client) stores everything in a local leveldb which is a file based database. Generally it will put it into ~/.ethereum unless you provide --datadir cli option.
Peers on the chain exchange information via a p2p protocol in a form of blocks that contain transactions. These are the then stored into leveldb once processed.
Everything you need to know about this process is explained in Ethereum Yellow Paper https://ethereum.github.io/yellowpaper/paper.pdf
