To boot a backup without a modchip, you'll need to use a boot disc called psx-change. You can't burn this disc though, or it won't work. you'll have to buy it or something. Or you could perform a manual swap trick, which requires swapping the backup with an original 2 or 3 times to boot it, and it means u have to remove the disc while its spinning. So i'd go for the boot disc, it's not like they cost much
You can burn games with Nero, this is what i usually use because its so easy (and my burner isn't compatible with clonecd). Clonecd is probably the best for burning PSX games though, but the compatibility rate with burners is not as good
CDRwin is also a good program, actually better than Nero for PSX games i think, but i've never had any problems with Nero.
I'm not sure on what u mean by "Does the boot sequence have to be on every 'back-up' disk?".