1. It means that Pete heard a pop song and didn't remember it exactly or didn't pay enough attention. Then he wrote his own song based on what he thought the pop hit was, and as a result he wrote a fairly original song.
As a songwriter, I do this a lot. :)
2. Yes, plastic punk means fake or "inauthentic" punk music - something polished for a mainstream audience. You don't need to take "offering" literally - it just means song (ie. a product) here.
I understand a "Daily Mail rage" means "irrational anger". I don't know if this refers to the journalists of the publication, or the readers who comment.