Buy shipyatds

I don't think that is expected behavior.  You cannot diplomatic trade for shipyards.  You can rush buy them for 750bc if your planet is not sponsoring another shipyard. 

I think it is intended that they cannot be purchased. It would be far too easy to exploit the AI if you buy their starport right before declaring attack so they have no way to build additional forces.

You can buy AI's constructors, though, which you can build a shipyard out of--for a steep price.  Unless the AI has a negative money balance, in which case he will give it to you for free.  

The planet flipped but the shipyard did not so now I want to buy it without having to go to war to destroy it.

In the diplo there is remove your ships from my territory. does this work for shipyards or does Stardock need to modify it.

Another option would be a VERY SLOW culture flip to a certain percent till can buy it. It would not flip all the way.

"The planet flipped but the shipyard did not so now I want to buy it without having to go to war to destroy it."

Or you could kill it with a privateer fleet.  

It is annoying that the AI players never decommission their shipyards after they lose the nearby planet or planets that were sponsoring them. They also don't try to unanchor them and slowly move them to their nearest colony.