Air pump revival
 

I just bought a 1988 fc convertible and I noticed the air pump belt is missing, the belts squeel while accelerating and I need to pass smog in California so I need to have all my emmisons in working order, I don't know what it needs to be fully hooked up so that is what I need help with, I have a racing beat exaust too. Cold starts are a struggle also but not warm. I will be posting pictures, I would appreciate some help, sorry if I'm not beng very specific.

Does the hose that feeds the cats and gets back pressure for the aux ports come straight from the air pump or the acv?

front of air pump goes to the air box.
Back of air pump goes to the ACV.
the split air tube( cat converter) hooks up at the rear of the intake and there is a small Nipple on the steel line that goes to the 5/6th port line that activates the ports.

The guy took to stock airbox out, Is it okay if I put a tube running to a little intake filter as a substitute ? I put the air pump belt on and it has a surging idle now when warming up? Maybe tps or could the air pump mess with the idle?

If the diapragms in the air control valve are torn they can cause vacuum leaks. The light pressure from the air pump may exaggerate these. Be sure the vacuum lines are all hooked up correctly. A smoke machine is very nice for checking leaks especially in the acv without having to disassemble it.

Previous owner said he drove it without the air pump belt for like 2 years

On my 88 t2 the air pump came "disconnected",meaning there's no pulley but the units still in the car,there is a block off plate up on the intake and the nipple next to it is plugged,that means some of my emissions are deleted right? But I still had the tube going to my exhaust,since I'm making a custom exhaust can I get rid of this entirely? Or keep it and get a belt that goes to the air pump?