Yes, miners may freely select which transactions to include in their block. They may choose not to include some transactions, or could even build an invalid block that will get rejected by the network.

However, if the censored transaction pays a sufficient fee, another miner will pick it into a subsequent block instead. It would take a majority of the hashrate acting in concert to reliably enforce censorship across the network as they would need to reorganize out any blocks by miners not participating in the censorship. In defense, censored spenders could raise their transaction fees to make it more attractive to defect from the censors. Assuming that any parties that might be subject to such censorship already avoid address reuse, such an attack would be generally fairly ineffective.

Any individual miner can choose which transactions it includes in the block it is trying to find the valid hash for. The usual criteria is to simply grab the transactions that pay the highest miner fees, but any other criteria can be followed.

So, the answer to your question is yes.

But. unless the miner is evil and has >50% of the total hashpower, the "victim" transaction will eventually make it into the blockchain through another miner. So, as long as the majority of hashpower doesn't decide to censor something, it won't practically happen.

Yes.

Remember this mess?

Luckily Marathon folded after a good deal of outrage from the bitcoin community.

Technically, yes, and they kind of do it all the time.

If you submit a tx without paying the fees, your tx will very likely never get mined.

Miners invest a lot of money to run their expensive business. It's a very competitive environment and censoring based on addresses is self harming.

Yes, A solo miner can choose which Transactions to include.

It depends with a pool miner. Historically pool miners get the transactions from the pool custodian and don't have a choice. In the future Stratum V2 will allow miners to choose their own transaction set.

Absolutely, yes, insofar as they can refuse to include a transaction in a block (hat tip @bass)

Try submitting a zero-fee transaction. You'll probably find it gets censored by many miners :-)

However there are also many miners who would include it, in order to claim the tx fee. It is assumed that miners are motivated by profit-maximisation.

In the end, the miner (or pool) with the most proof of work can choose the transactions to include, which could include zero transactions, eg in the case of an attack.

No, miners cannot censor transactions on the Bitcoin network.

Transactions are broadcast to the network and confirmed by miners who add them to a block and publish it to the blockchain.

Miners do have the ability to choose which transactions to include in a block, but they cannot censor a specific transaction without risking the integrity of the entire network. The decentralized and open-source nature of Bitcoin makes censorship difficult, as any attempt to censor a transaction would likely be rejected by other participants in the network.