About relatives pronoun with BeV

The given sentence means that out of a group of guys, the one who's your brother is playing the piano. [Restrictive clause]

If you set off the who clause with commas, you'll merely be providing extra information (that he is your brother) about the guy playing the piano. [Nonrestrictive Clause]

If this doesn't make it clear, consider these sentences:

My brother who is a doctor lives in Grenada. [Restrictive Clause]

My brother, who is a doctor, lives in Grenada. [Nonrestrictive Clause]

The first sentence means that you have many brothers and you are identifying a particular one among them.

The second sentence means that you have only one brother and you are merely providing additional information about him. The part set off with commas can be removed without affecting the meaning of the sentence.

No, you can't always remove WHIZ - your second sentence is barely grammatical for me: I can only read it as my brother in apposition, normally preceded by a comma.

You can drop the WHIZ before a participle (present or past), or a prepositional phrase, but not normally anything else. See https://www.grammarwiz.com/reduced-relative-clauses.html