UPDATE:

Just took it for a test drive and it started up fine, took it out of the garage, drove down the block about 1/2 mile and it died. Then I restarted and drove it back and parked it in the garage.

Got a new code - P0418 --> Secondary Air Injection Sensor A Circuit Bank 1 or Single Sensor. I hear a vacuum sound coming from the AIR pump and it stayed on for a few seconds after shutting off the car and putting key to OFF position.

Sounds like this operation of the SAI pump is normal for cold starts, but is the code indicating a bad solenoid, clogged filter, or loose rivets?

I also discovered the source of my faint beeping in the engine fuse box - Relay #10 for the ABS. I tested it again and it tested OK for continuity and closing when 12V applied across smaller terminals. I replaced it with another one and it still beeps. Now if I push down on the relays they start to click and close.

Still getting codes P0340, P0418, P0560, and P1536.