Does DATABASE Full Backup break the Log Chain Sequence Number (LSN)?

No; This is not TRUE. Initiating a full back up outside the schedule will not break the LSN, hence this will not impact your point in time restore of the database.

But this could impact your RTO if “Differential Backup” is a part of your backup strategy; this is because ad-hoc Full Backup will change the first LSN.

Here we can see that First_LSN changes with every Full back which impacts the RTO.

You cannot apply transaction log backup on the top of Copy-Only Backup

Incorrect – YOU CAN APPLY (*.TRN)

Can I initialize my Always-On Database Copy_Only Backup?

No, Database cannot initialize for Always-On with Copy_Only backups.

How the Log backup behaves on Asynchronous Replica?