If this is being spoken, I would say this works well. "Wild" might be a more natural choice, but may imply the monkey is in a rural area, or one populated by no (or very few) people. If you are typing, as others suggest, the hyphen is probably not necessary in a casual context. In short, your sentence was very good!

'Free roaming' is a good way to describe them. Some other adjectives could be a 'wild monkey,' 'street monkey,' or a 'feral monkey,' depending on how the animals live. A 'feral monkey' would specifically be a monkey that is descended from monkeys that were domesticated/previously lived with humans, but they have since returned to the wild. Typically, 'feral' is used to describe cats and dogs that live on their own with little to no 'help' from humans. 'Wild monkey' just implies that they live naturally in the environment, and they aren't pets. Wild animals will generally be more afraid of humans. 'Street monkey' implies that the animals are wild, but their environment brings them into frequent contact with humans, so they may be less afraid of humans, regularly approach humans for food, etc.

The hyphen is correct and the tone is already casual, but it doesn’t have a clear meaning. ‘Free-roaming’ usually applies to animals that people eat, so it doesn’t precisely convey the situation of the monkey. Also, what do you mean by feeding it, and what is the significance of feeding it? A meaningful example using some of the same words: Yesterday, I added feed to the trough of our free-roaming cattle. They eat more than just grass.

Sure. The hyphen is not necessary.