Phisherman writes:

A garage-door mechanic will replace BOTH springs (as it should be
done) for about $200.

Should be less than that.

The garage door mechanic will have the correct spring.

Not necessarily.

2. Are there some modern thingamagiggys for winding springs that are
safe?

The garage door mechanic uses two round metal bars, perhaps 24" long.

The standard winding bar for residential doors is 1/2" mild steel, 18"
long.

3. How unsafe is the process of winding springs

Safe for a garage door mechanic. Not safe for the typical home owner.

Over 1000 correspondents happily tell me they did it themselves.

Call a pro. I know someone who got his thumb torn off messing with a
garage-door spring. He is lucky to be alive.

No, he got hurt by ignorance of proper technique.

I have spent years trying to sort through the friend-of-a-friend horror
tales to get to the truth of injuries from torsion springs. I have
collected a few reliable first-hand accounts of injuries. The cause
seems to be simply not having the simplest of tools and techniques.

Typically, someone is hurt because he loosens the cone setscrews without
knowing to engage a winding bar first.

5. Are these different quality springs, is it the kind of business
where you get what you pay for?

Supposedly most of these are made at the same place.

There is a wide variation in service life. Price has little to do with
it. See my page:

http://www.truetex.com/garage.htm