The rent covers PITI and utilities with a little extra built in to cover anything over the average utility usage.

He has already verbally accepted, but I'm wondering if it's worth to go the extra step?

This is an opportunistic strategy with a lot of moving pieces and the riskiest of all investment strategies in the real estate universe (the safer ones being core, core plus and value-added).

Maybe an extra $150 per month?

On your homeowner financing loan alternatives is to show them the math on paper that shows them the extra profit and the possible tax liability spread out for several periods instead of showing they will and have to report it all in the next year end tax preparation and the savings that they might get. 

Advertising costs alone can run in the hundreds a month for a single unit; StreetEasy now charges $3/ad/day; that's $90/month for one ad only!

I want to start getting into real estate as to make some extra money apart from my full time job?

The main key to your performance is great photos and little extras that push you to the top.

1) at $23k there isn't a lot of room to negotiate down especially since there are closing costs and the seller has to move, so I'm not surprised they won't go down. 2) from the description it sounds like it needs a lot of work and adding a closet (literally just some studs, drywall and a door) is not going to cost much if you do it while you are tearing up, replacing and fixing up everything else.Are you sure the issue isn't just that it's your first and you are getting nervous? 

Even though it prints out on a separate page, I don't charge extra for that.