I would call Neons a good car, especially if the engine has been rebuilt, and the answer to each of das2123's questions is an affirmative, "yes that was done". All of those are problems that Neon's were subject to, though on most cars I would think they have been done. We have a 1997 SOHC 4 door Neon.
A "mil trouble code" refers to the information the computer can show you. The computer is called the Powertrain Control Module, & I believe is located on the driver's side of the engine compartment, halfway between windshield and headlamps atop the inside fender.
There are trouble codes that will result in the Maintenance Indicator Light coming on, to indicate the computer thinks something isnt right. You can get the codes to read-out, by turning the ignition from off to on to off to on to off to on (and leave it in the on position) within 3 seconds, but without starting the engine. Then count the flashes of the Maintenance Indicator Light (or check engine light). It will blink out two digit codes, like a 12, a 31, a 55, etc. If the MIL light isnt on, check the codes anyway.
Then let us know what you get. There is a listing of what the trouble codes are somewhere on the internet, but I forget where they are located.
Also, you can usually get copies of the original Dodge Neon Service Manual from ebay.com. They are really worthwhile.