Why does a burner lock-down?
This can happen for a number of reasons please be more specific as to what is happening at the time to cause this.
Why can only some CD players read CDs created using Nero or InCD?
I'm not sure what you mean by this but I think you just mean InCD. InCD is a packet writing platform which treats your CD/DVD as a hard drive so only burns the data to it as and when you request it. Until you close the session the CD/DVD will only be able to be read in the CD-RW or DVD-RW drive.
Nero on the other hand will create CD's or DVD's that can be read in almost all players, I say almost all as some old CD/DVD players refuse to accept burnt media.
Kind of a spinoff of #2...If you format a CDRW using ROXIO, will other CD drives be able to read it if the CD is not closed?
In theory if you try to read the disc in another cd-rw or dvd-rw drive with the correct software installed on that machine then yes it should work but I have never tried this so I'm unsure of the answer but I imagine that this could be problamatic between different drives. The best bet is to just burn to a blank cd-r as these are now so cheap or to a cd-rw disc rather than using InCD.
If there is a reason as to why you need to know this please let us know your reason and we might be better able to help you.