Furnace Troubleshooting- Inconsistent Error Codes
Yes it sounds like the pressure switch may be working correctly. If you'll be in constant attendance and feel confident about your ability to detect any problems, you could use a jumper in place of the pressure switch. You'll likely find that the controller verifies that the switch is open when the inducer is off and closes when the inducer is on -- so the jumper will have to be placed and removed at the right times.

The fact that the furnace sometimes ignites but other times not, and that sometimes the air blower remains on, suggests to me a problem with the flame proving function. Maybe have a look at After blowing heat the fan won't stop, continue blowing cold air for prolonged period of time (30+ min). Power cycle the furnace and observe its operation through several run attempts as described there.