Fan shouldn't run with key on. I'd unplug that fan for now and figure out why it's on constant.
As for the light on dash, that is normal is normal, as long as it goes out when engine starts.
For cold temp starting, press gas pedal 2 or 3 times to the floor, then release, and keep your foot off the gas until it starts. This primes the intake with fuel from the accelerator pump, and sets the choke open. It may sputter out after catching, just repeat procedure until it catches well enough to begin the high idle. Let it warm up 5 mins before you drive in cold weather.