All this is my own thinking, not to be taken as Halacha.
A father marrying off his young daughter. (Was this allowed after the churban? Is it now? When the change? The change implemented by whom?)
Yes, yes, and no change.
It creates problems when parents are divorced, and the father marries her off in spite.
Some people believe today a woman has a right to a ‘get’ upon demand. Any halachic basis for this belief? If so, what is the halachic basis?
No, yes, Beis Din has the right to force it if he acts improperly (which will change with the times). Also Rabbanu Gershom has a Takana that you have to have the wife’s agreement to divorce (IIRC).