Mining without full node In my understanding it should be possible to run stratum server over some kinda limited node (the one that doesn't carry whole blockchain) since stratum doesn't need many functions from the daemon... I'd guess getblocktemplate should be sufficient for mining.

In my humble estimate, I can see it should be enough to store just X last blocks instead of having the whole data for the mining purpose. is that correct? (yes, I do know the difference between full node and thin-client)

What's gonna be the best way to setup thin client and mining pool without waiting weeks for it to sync with the net? Is there any API for that maybe?
You can use a node in pruning mode. In Pruning mode, the node will delete the blockchain data that it no longer needs. It is still a full node as it still has to download all blocks and transactions and then verifies them. But it just doesn't store the entire blockchain.