Question on Destroying My Own Buildings

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.

Not quite.
If you convert, the convertibles are converted but the non convertibles disappear and will not give you any funds. So you probably want to destroy those manually the turn before conversion is complete.

Also, those that can be converted often may end up as a lower level building, especially the barracks range, as cities have different level thresholds than castles (for instance you can build quite advanced barracks in a fortress or citadel, but if you convert them to minor city, this gets dropped down a lot).

As for auto-repair, not sure, as I always repair immediately. I assume that those that can be converted are auto repaired, but don't quote me on that.

Oh, and make sure that you don't have a chivalric governor in town when destroying buildings, he may become more dreadful.

Walls are repaired when converted. When you capture a castle that you plan to convert to a town, you can leave the walls unrepaired. I am not sure however of other buildings (i.e. ballista makers, and armouries <-- sp?)