What's a fish's range of vision? Do they usually see to the sides and in front?
I would believe that varies considerably species to species

.
For example, due to where the eyes are located, a silver dollar (
Metynnis argenteus) is going to see differently from a mudskipper (subfamily
Oxudercinae) which once more will see differently from a four-eyed fish (
Anableps sp.).
Do their eyes move together or can one look back and the other forward?
That would also depend on the species of fish.
It has been found, however, that fish can prefer to use a different side of the brain (and consequently a different eye) to look at different kinds of objects.
A relatively recent issue (7th July 2007) of 'New Scientist' had an article on this.
According to the article, a paper by Culum Brown and 'his team' (
available here) shows wild caught
Brachyrhaphis episcopi from areas of high predation preferred to use one specific eye to view a 'novel object' (a yellow cross) while those caught from an area of low predation showed little to no preference.
The article also says the lab raised offspring from each group of fish showed similar results to their parents, but I can not find this in a paper on the web.
All of this goes to suggest that each eye can be used independently. Indeed if you observe fish in your aquarium, you may notice that each eye is pointing a different way - while evidently still in use. So yes, one can look 'back' and the other 'forward'.