Question on Destroying My Own Buildings

[grapedog]

When taking over enemy castles, most of them get converted into cities. For some of the more advanced fortresses and castles that have ranges and stables, destroying those buildings is essentially just free instant money once it's turned into a city, is that correct? Does converting a city automatically give you cash for all the un-usable buildings that get scrapped?

Destroying a castle barracks seems to leave the city without it's similar building once converted, or am I wrong?

Also, do all buildings that are being carried over, get repaired when converting(like ports/mines/religion etc.)? If they do get repaired, is it free or does it take it out of the budget?

Anything else that I should know that I'm missing? I tried searching for these things in the forums, but I couldn't find the answers among so many returned results, so I appreciate the help.