As far as marking, my recently rescued little guy is about 5 yrs old; foster mom had him neutered right before I got him. She said he did mark before neutering but almost totally stopped after that. I keep a belly band on him if I can't closely watch him, and I've only seen two spots on it that were probably marking (not enough for pee). Also my daughter's silky terrier was the worst dog I have ever seen for marking when she first rescued him! He would literally run through the living room with his leg lifted, leaving a trail of marking on the sofa or any other vertical object! It was crazy...but as soon as he was neutered he almost totally stopped marking. Of course, like another post said - you do have to be prepared just in case. Belly bands are wonderful!
He might be micro-chipped which would help if he has been stolen...the vet could tell you that. Either way, it's an opportunity to rescue this little guy. So sweet that your son is willing to spend his birthday money to help...what a wonderful, caring thing to do. Let us know what happens!