1992 Chrysler 5th Avenue Stalling, running rough, hard star

I have one or two problems that may or may not be related. At times during cold start the car will start okay, will fluctuate in RPM almost like a choke not adjusted properly and choking itself. You cannot clear the condition by holding the gas pedal to the floor as you would a sticking choke. The idle will correct itself after the car has ran for approximately 5 minutes and then run smooth. After that the car will at times stall when slowing down approaching a stop light or turning corners but restarts okay. This is a intermittent problem and is more noticeable in colder weather conditions. I have ran a code scan and their is no history or current codes. I am thinking that their may be a IAC motor issue, any input would be appreciated. Secondly it is also noticed that the car will stall when it gets below a half a tank or mostly at a 1/4 tank or less. Once it is filled up the car runs okay. Again this is a intermittent problem. There is no visual leaks at the tank or filler tube areas. Again no codes noticed on a scan. I am thinking a possible sock or filter issue on the electirc fuel pump sending unit. Any response would be appreciated. Thank you and do have a great day!