FLYWHEEL MAKES RUBBING NOISE WHEN WARM AND ACCELERATING

If the Bendix arm of the starter is not meshing properly with the teeth of the flywheel, you may have improperly installed the flywheel; you may have the wrong starter or flywheel...it is always best, when removing parts from a car to visually match the new one up to the old part, side-by-side. Any deviation in design of the replacement part to the original will not work.
The other possibility is you either forgot to place the original spacers (if there were any) of the old starter onto the new one; or as you mentioned in your post... you will have to add shims.
You never mentioned whether the parts were bought through a 3rd party vendor (auto parts store) or if they are genuine Nissan parts obtained through the dealership's parts department.
It is not unusual for a counter person at an auto parts store to make a mistake and give you the wrong part. Sometimes vehicle manufacturers may retool design in the same model year and unless there is a footnote in the parts look-up book that discloses this, you may have gotten the earlier production part vs. the redesigned one.

The alternator flywheel? I believe, correct me if I'm wrong, that you are referring to the wheel on the alternator that the belt goes around. The screeching indicates a loose or possibly worn drive belt. As the belt slides instead of engaging, it screeches until the rubber gets hot enough to finally grip. Eventually, your battery will fail to charge. It could be a simple adjustment is needed via the alternator or a tensioner to tighten the belt. However, If there's any question about the age or condition of the belt, better to replace it before it breaks. This would be important so you can see how it wraps around the various components. The folks at an auto parts store should be able to assist you with this.

Flywheels very seldom give a problem and have nothing to do with acceleration problems . If it was loose you would have massive vibrations and would know of a problem . If it is an automatic the so called flywheel ( flex plate) have a tendency to crack at the crank mounting bolts and the cracks radiate out to where the torque converter mounts on and then there will be no drive or start action as the ring gear just falls away from the starter. The noise may be from the plate starting to fail so remove the inspection cover and check the plate for cracks or rust streaks which are cracks that you will not see.

recheck the parts to be the correct ones because what you are describing is a gear mesh problem. ensure the gear on the starter matches those gear teeth on the flywheel. once you know they are matching and are correct for that year and size of engine, you will need a variety of shims to set the distance between the two correctly. (which you already have experience at). But it is important you have the correct starter because the solenoid and the throw-out spring are specific made to travel a set distance. If that distance is not far/long enough the gear will not full engage the width/thickness of the flywheel tooth/teeth (which causes the starter gear to strip those teeth of the back side of flywheel). SO you need to do some serious looking at those parts and the meshing when solenoid is engaging.

I would need to inspect the problem to even have a guess as to what you did wrong or if the part is incorrect for the application.

when you had the starter out, did you inspect the flywheel itself? the starter can be engaging but the flywheel can have some wear so that a grinding noise will be heard

The starter should have been mounted with a thin "shim" plate between the starter and the bell housing. (flywheel cover). It moves the starter out away from the flywheel. If your auto parts guy doesn't seem to have one, you can make one out of thin metal the thickness of a matchbook cover. Insure the starters housing is metal to metal with it's mount for good electrical contact.

Sorry about the theft, I know the feeling. You may want to take the starter back out and bench test it, Find out if it was assembled correctly (meaning is the pinion gear throwing out far enough) take a measurement from the pinion gear to the flange and compare it to the distance from the flywheel to the case. It is possible the starter is wrong too. Take a look at the face of the pinion gear and flywheel and see if the gear might be the wrong size.

Hello, I would make sure that your car is not one of those half year cars becuase two differn't starters may be offered for the same year of car. Also, I would check and see if your battery has enough CCA's to power your system. The only other thing is to turn your crankshaft with a breaker bar to turn your flywheel to possibly get a fresh area of teeth on it. If none of this fails it's as simple as just replacing the flywheel. If you did a bench test on the starter and the bendix engaged that is good. Buying parts from an Auto parts store does not gurantee the part is good and that the bendix engages the full distance to turn the flywheel. I would try to find a mechanic who rebuilds starters to make sure that the bendix is engaging fully. I hope this helps you!

You don't think it might be the power steering pump making that noise. It could be flywheel. Tell you what, if it is flywheel hears a way to chk. (outside of going underneith car), have you ever powerbreaked a car? setting still, step on break hold it down firm put it in gear and start giveing it throuttle do it in forward and reverse you might have to give it alittle more throttle than your comfortable with but thats the way your going to find out if its flywheel it should start making that noise or sound like a rod nocking or like your hitting a piece of metal with a hammer something on that order. Try that and see what happens Best to do this when there is nothing infront or behind you.