This sounds like a horrible idea.

The cat will ONLY be allowed if it is spayed/neutered (I've dealt with cats in heat and it is horrible).Should I stick to my guns and say no or allow the pet because I get extra money and this tenant has been a model citizen?

They will call code enforcement and even bust out a window, just so that they can tell the inspector what a horrible landlord you are.

I can see the uphill battle on the internet is a real problem for newbies, from poor advice to bad to horrible is never ending.

The closest exceptions may be attorneys, it's the nature of their profession to represent others in the best light regardless of the client's sinful nature and their reputation socially may be horrible, professionally could be a different matter. 

Just because a bank will give a loan doesn't mean it's a deal and I have seen lenders fund some horrible deals before.As for tenants with bad pasts it is a rare occasion where something works out.

Cars from this era were often horrible, especially the American ones.

I had a HORRIBLE experience with Hometown title.

It was not our fault that they had to hire more sub contractors to fix their own mistake.In addition to the horrible customer service, they were condescending.  

The presumed fact that this new generation is being taught no real values and can be so careless to "forget" that your precious child was left ON THE ROOF OF YOUR CAR is horrible.