One guy who lives behind me on the next street up says it is his property. He says he had it surveyed and it is his property.
If he is telling the truth that he had it surveyed, the surveyor might (or might not) have made a mistake. I would find out whether the surveyer was aware of the alley having been there. If so, they surveyer might have found out something about it that you don't know.
1.Since no one owns it how does one go about claiming it and start paying taxes on it?
As you know, adverse possession doesn't work against the government. You need to ask the Borough to "vacate" the alley. There will be a procedure to do this. Ask them.
2. Does this guy have any legal right to say he owns the land when it is not on his deed nor is there any record of him claiming it or paying taxes on it.
No; he doesn't own it even if he had paid the taxes, for the same reason noted above.
3. Shouldn't it be since it was an a abandoned alley shouldn't everyone get an equal piece of it if they want it? Out of the 6 houses 5 of them border the alley in one way or another, so shouldn't all 5 get an equal share of the alley that is if they want it?
Probably that is the way a vacation would work. It depends on how it was originally dedicated as an alley. If there was a plat, for example, showing all of your lots subject to a right-of-way for an alley, upon vacation it would go back to each lot owner.