Svtkobra, I like the vent locations you and Dawg have decided on. I think you should get a decent cross flow of air running diagonally side to side and bottom to top.
1) I agree passive venting would be best if possible, if for no other reason than to remove a point of failure. It would be a shame to depend on a fan (that could fail) for cooling if you could get by without one.
2) Go for the simplest vents you can find, the ones you posted have dampers built in. Dampers are great for choking down air to balance an air conditioning system, but you're shooting for maximum air flow not trying to control or direct it. Search for a return grill, maybe even scratch off returns with filter holders if you don't need one. I'd go for something like this:
Value Brand Return Air Grille, 16x16", White 373692 | Zoro.com
...as an aside I like Zoro a lot, owned by Grainger, with the same stock, but better prices.
3) As to vent size, I think Dawg is also right go big, especially on the utility room side. something 16" wide would be a good choice because you can cut out the space between two studs and screw the grill through the drywall and directly into those studs. Pre-drill the holes.
I think even without a exhaust fan or the AHU pulling, warm air will pass over to the utility room which is essentially open to the rest of your apartment with its louvered door.
4) With server fan orientation: try and find out. I think pulling over the motherboard and pushing though a wall of HDDs and a back plane wouldn't work as well as pulling through HDDs and over the motherboard. If you keep disk trays empty it might work well, I say test and see.