The reason the F-20 wasn't put into production is the USAF wanted to drive down the cost of the F-16 by making everyone buy them (The more you build the lower the unit cost, over time). The F-20 actually had some more advanced technology at the time than the F-16 and the production model would have had a larger wing. However, other countries wouldn't buy an aircraft the USAF didn't buy (If the USAF buys it you know there will be plenty of spare parts available into the future) as the USAF chose a stripped down lower cost F-16, that was actually mostly useless, instead of the F-20, as for the Air Defense Fighter program. After the F-20 program was cancelled, IIRC, the ADF F-16s were quickly retired. The fact is, the F-16 was overkill for what many countries required and the F-20 would have had lower operating costs. Having said that, the F-16 is still one of the greatest fighter designs ever, IMHO.
Regarding the service ceiling, it's the height at which the aircraft can no longer climb more than 100fpm for propeller driven aircraft and 500 fpm for jets, IIRC, at cruise/continuous power settings. In afterburner, the aircraft should be able to attain higher altitudes, which is why so many fighters can zoom climb to 80000 ft.