I can only speak about Western-Europe because that's my specialization, but no. I'll explain by summarizing what happened before the 1800s, but I can't really cite my sources since these are things I remember by myself. If you want, I can look it up anyway.
In the middle ages, people married people of their own age. Exceptions were when a 37 y/o man's wife died (most women of his own age are already married, and some other reasons) or when we're talking about court marriage. But even when it comes to court marriage, it didn't happen very frequently. It happened more often that two children married.
In early modern times there's something we call 'the birth of the child'. During the middle ages, a child was not seen as a child, but as a smaller version of an adult. There's was no difference between children and adults, except children still needed to learn a lot. After the middle ages, people started to realize that children had specific needs, so they made toys, schools, etc. Something else important was the fact that the age of marriage got later (twenties), and that there were all kind of activities organized for teenagers, so they were able to get to know each other in a proper way. This way, marriage between persons of the same age was common.
In the 1800s, after the industrial revolution, this whole culture of wooing disappeared. Poor people didn't really care about who they'd marry, because it was a labourer anyway (this is a simplified vision, because there's still something called 'love', but I hope it's clear). Rich people cared about who they'd marry, but they often went to school until a reasonable age, so they weren't really able to marry at 14. Also, the girl's father had a say in his daughter's marriage. Rich fathers wanted sons-in-law who could take over the company, if needed. He had to be young and educated, in order to do that. So no, mariage between a 37 y/o man and a 14 y/o girl was not a habit in the 1800s.
To answer your question whether it was morally accepted, it's easy. Ephebophilia (a relationship between an adult and a teenager) is biologically normal (if the 14 y/o girl's already on her period), but it didn't occur in society. This means society didn't morally accept it.
I hope I helped you. :)
This question is largely answered in the FAQ
The answer is normal no. Morally acceptable depends on the area but in most areas it would be frowned upon but not considered entirely wrong depending on the circumstances.
I'm guessing from the ages and time frame you are specifically referring to Joseph Smith Jr. In that particular case it was considered wrong because of the polygamy aspect. Joseph Smiths actions in trying to cover up his polygamy, including destroying the Nauvoo Expositor, indicate he felt that the larger community would think his polygamy was wrong.