I purchased a 81 Spider 2 years ago with the intent of selling it. I have a couple of old 60s Cadillacs and Fiats were not really my thing. After driving it once, I knew i was hooked. It is now a permanent part of the family. The car runs great but I am now starting to have problems with it not starting and it just dies randomly.
PROBLEM #1
The solenoid is engaging when i turn the key but the starter does not turn. I will turn the key a few more times and then the starter will turn. This is a new starter. This does not happen all the time but mostly when warmed up and at the most inconvenient times.

PROBLEM #2
This problem just started happening. The car will be at idle or highway speed and will just die. The time it happened on the highway, i had complete loss of power and it felt like i had cut the ignition by turning the key off. Then all of a sudden power kicked in again.
Sometimes when the car is idling, it will just die. It will start right up again though.
I thought initially fuel pump. When i turn the ignition on, the fuel pump goes on and stays on. Is this normal? Is there nothing that turns it off once it builds up pressure?
Thanks for anything you can help me out with.
Regards,
Todd