The Burbs

My husband and I are considering moving to Parma, the Pleasant Valley Road area to be specific.  We're curious whether there are ordinances related to the following:

Is there a limit on the number of dogs permitted in one household?  We have two old dogs and a little dog and need to know for their sake.  I know there's a restriction on barking but that's all I could find about dogs.

Is there a requirement for dogs to be contained within a physical fence, or are invisible fences permitted?  Our dogs are currently on an invisible fence and the house we're looking at doesn't have a fence in place.

Is there a restriction against outside cats?  We have two that are indoor/outdoor and may need to find someone to keep them here if there's a likelihood that they'll be trapped and euthanized.   

I appreciate your help in this matter.  We haven't decided whether to relocate yet and this may affect our decision on where to move.