96 Monte Z34 3.4. The car is hard to start when cold (starts then stalls) but eventually after the 3rd time it will stay running but after it eventually starts it will stall at every stop unless you keep your foot on the gas and then the idle will jump up when moving. Code is 0410 and I found out from searches that means the air pump is most likely bad. The Air pump fuse keeps blowing so I'm assuming the pump is bad. My question is will the air pump cause the problems? No where did I read of anyone having a bad air pump with any symptoms except the service engine light on.

I don't think the AIR system is your problem, sounds like a sticking egr valve or a iac not operating, pull them both out and check for carbon build up on either one, particularly the egr. A full scan may reveal other problems that could cause this, a code reader is not going to see whats happening here.