Block Validation: who does it? How much it costs? And is it present in all protocols? Different threads were posted in order to clear up this question, but there are some points that I would need to confirm: 


When you become a full-node (NOT miner, you just downloaded the full blockchain with a wallet or smilar), are you automatically a validator? Meaning that every new block will be validated by you (and the rest of full-nodes) in order to publish to everyone else whether is trusted or not. Or it does not exist someone that can be only a "validator", and only miners can be also validators?
Does block validation process spend too much energy? Or validate blocks is not a "big deal"?
In protocols that use PoW and PoS/DPoS (Bitcoin, Ethereum, Cardano, EOS...), once a block has been constructed using one of those consensus methods and included into the chain, will be always being involved this "second" validation for the rest of the full-nodes in that particular blockchain network? (I suspect that this second validation could be work slightly different in each of them, but always including this validation for the rest of the nodes)
And finally: what happen if one full-node start to rejects new blocks (he/she considers that are not valid), but the rest of the nodes says that is correct? Imagine a troll/hacker that starts to say that all the nodes are invalid, can that people be banned? Or will be that person just ignored?
When you become a full-node (NOT miner, you just downloaded the full
  blockchain with a wallet or smilar), are you automatically a
  validator? Meaning that every new block will be validated by you (and
  the rest of full-nodes) in order to publish to everyone else whether
  is trusted or not. Or it does not exist someone that can be only a
  "validator", and only miners can be also validators?


Yes, all full nodes validate all transactions before putting them in their mempool and all the blocks they receive. You do not publish to anyone if it's trusted or not, everyone checks if it is valid by themselves.


  Does block validation process spend too much energy? Or validate
  blocks is not a "big deal"?


No.


  In protocols that use PoW and PoS/DPoS (Bitcoin, Ethereum, Cardano,
  EOS...), once a block has been constructed using one of those
  consensus methods and included into the chain, will be always being
  involved this "second" validation for the rest of the full-nodes in
  that particular blockchain network? (I suspect that this second
  validation could be work slightly different in each of them, but
  always including this validation for the rest of the nodes)


Not sure what exactly you mean here. Every full node will validate all blocks once.


  And finally: what happen if one full-node start to rejects new blocks
  (he/she considers that are not valid), but the rest of the nodes says
  that is correct? Imagine a troll/hacker that starts to say that all
  the nodes are invalid, can that people be banned? Or will be that
  person just ignored?


If someone rejects valid blocks he will be left behind as the other nodes will continue to build their chain. No one asks anyone if "other nodes are valid" or "other blocks are valid", they ask each other for blocks which they verify themselves when they receive them. If he tries to provide an invalid block when asked for one he will be banned by other nodes. That's the whole point of bitcoin, you don't have to trust anyone, you check yourself.