First of all, there's no regular character named Paul on Family Guy, there's been several one time characters.
Second, the only episode you could possibly be talking about is the episode where Stewie and Brian remodel a house. That would be Season Six|Episode Seven Peter's Daughter
See the provided link
Mind over Murder
Family Guy Petoria Episode.
Don't Make Me Over
Mind Over Murder
The 255th episode aired on Family Guy was "Peter's Sister"
No.
There have been well over a hundred songs featured in Family Guy episodes over the run. Your question cannot be answered as you didn't specify which episode you're referring to. You'll have narrow it down to one episode.
Don't Make Me Over
season 10, episode 22. Family Guy Viewer Mail 2
Season 4, Episode 4 | Don't Make Me Over
It is an episode of Family Guy
Family Guy Viewer Mail, season 3 Episode 21