If I pleaded guilty to a crime, when I fill out an application, what do I put on the application about felony convictions?

A guilty plea is the same as a conviction. You must disclose the felony. There is no law governing decisions to not hire or to discharge for falsification of an employment application, or what is lawfully required to be disclosed. What ever the employer says is final. No right to sue, no right to appeal, etc. You should look closely at the question asked, and then be truthful. I have seen valuable employees of 20+ years discharged for minor crimes that were not disclosed on the employment application. While many employees will overlook minor events, they will not overlook dishonest answers on the employment appl. When in doubt, disclose.