can they pick any valid transactions with significantly low fee? if they can, how all these things work? is it manually adding a list of transactions? or automatically?
If the transaction is valid, they can do it manually, even
if it does not follow the standard, but as mentioned above, the fees are the ones that govern and can be paid privately away from the transaction fees.
I remember a similar case:
~1 BTC Bounty For those who want details.
that is really messed up! every single documentation that i have ever seen has always said "it must not be compressed or it will not be mined". now i went back and checked the out, they are all are ambiguous about it!
take BIP143 for example:
https://github.com/bitcoin/bips/blob/master/bip-0143.mediawiki#restrictions-on-public-key-typeQuote
As a default policy, only compressed public keys are accepted in P2WPKH and P2WSH. Each public key passed to a sigop inside version 0 witness program must be a compressed key: the first byte MUST be either 0x02 or 0x03, and the size MUST be 33 bytes. Transactions that break this rule will not be relayed or mined by default.