Am I held accountable for everyone sitting with me if I play a YouTube video of a TV series or one that contains songs? And do I have to delete an audio clip I recorded for my relatives that contains music from the television, and then re-record it?

If a clip containing forbidden material is opened and others watch it, then the one who opened it is considered an assistant to them in sin, and a cause for them falling into disobedience; because the disobedient person incurs the sin of whoever caused him to fall into disobedience. Allah Almighty says: "That they may bear their own burdens in full on the Day of Resurrection, and some of the burdens of those whom they misguide without knowledge. How evil is that which they bear!" [An-Nahl: 25]. The effects of a servant's action, whether obedience or disobedience, are accounted for. Whatever results from a servant's action brings him reward and punishment, even if he did not intend it.

As for watching a forbidden clip in a gathering where there are others, without them watching it with you, or being affected by your watching it; in this case, you have not assisted them, nor caused them to fall into anything forbidden.

It is not permissible to send an audio clip containing music; due to the spreading of it, and assisting in listening to it.