I am wondering if all bitcoin miners need to be full nodes. Or is it possible for a miner to just download all the blockchain once, do all necessary computations to start mining and then delete the complete blockchain and only work on the "last blocks". I.e can a miner don't be a full node?
This is not a duplicate question.
If miners delete the blocks data, someone can fool them by sending a transaction that spends money it shouldn't be able to. In principle, some of them could do that and trust the other miners to validate transactions, but the more people do that, the more the whole network is vulnerable to fraud.
The same can be said for non-miners. If you don't run a full node, you're not actually running Bitcoin, but trusting people that run it to verify transactions for you.
Of course that's possible. A miner may be using SPV / keeping only the block headers*. The downside of this is that such a miner won't be able to include transactions of people s/he doesn't trust (i.e. not a trustworthy friend of the miner)
If that miner wants to take risk, s/he can verify the transactions that were relayed to him using online block explorers.
*: A miner doesn't even need to keep block headers. If he knows the previous block's hash, timestamp and network difficulty, that's enough.
