Are there animals / mammals which only have one eye?
All mammals have exactly two eyes, though the eyes are vestigial in some species, some of which are even blind.

Small fossorial (burrowing) mammals generally have very tiny externally visible eyes or eyes that are covered with skin (e.g. golden moles). Some river dolphins (e.g. "blind dolphins") also have very small, vestigial eyes.

Some reptiles (and amphibians?) have a "third eye" called a parietal eye. However, it isn't a true eye. (See How Humans Lost Our Chance at a Third Eye).

I'm not aware of any vertebrates that have just one eye. As far as I know, all vertebrates have two eyes. The anableps is a fish that is nicknamed "the four-eyed fish," or something like that, though it actually has just two eyes.

However, there are one-eyed invertebrates, including copepods. (One copepod genus bears the scientific name Cyclops.) Answering your first question, copepods reportedly lack depth perception. There may be other one-eyed invertebrates, but I'm not an expert on inverts (there are too many species to count let alone study!).