Pressure switch goodman furnace 100-4 blinks three times, installed new switch still wont start.Also does inducer motor start before gas fires??

2nd question first here: Yes, inducer motor (exhaust fan) must run before gas an fire.
MY FOLLOWING ANSWER WAS COPIED OVER FROM YOUR OTHER POST...
I'm going to assume you can operate and understand a VOM, as well as being able to observe the proper safety procedures for performing service work.

In the case of a control board returning an error code for a failing pressure switch, but the pressure switch actually checks out OK, try this:

Test your exhaust fan power leads for power coming in from the board during the first few seconds at the start of the heating cycle. If power is not showing up there, there is likely another circuit malfunctioning somewhere preventing startup. However, if power is showing up there, then deactivate the system and disconnect the exhaust fan power supply leads from the motor. Test the motor's coil for continuity - a failed exhaust motor coil will result in no vacuum for the pressure switch, hence no heating cycle allowed by the control board.

In my case, the exhaust fan actually failed due to a broken coil lead at the binding post to the push-on connector. I was able to repair the coil lead myself - at no cost - hurray!