Can cd rom drives usually read cd rw disks that have been burned in a modern cd rw or dvd rw drive and what are the determining factors?

Ok this one can be tough to answer.

The firm answer is "It depends". Regardless of the age of the cd rom drive the determining factor is "format". For CDs there are many, there are (without the quotes) "+R", "+RW", "-R", and "-RW". Yes the + and the - signs are there on purpose. A drive that can read/burn in +R can read +R and -R, and +RW and -RW. a drive that can read/burn in -R or -RW, can ONLY read -R and -RW.

If you look at your CD, somewhere on the label (and somewhere on the player usually) it will say if it's a + or - R. So if your drive is a CD-RW +R (or +RW) it can read either format. If it's a CD-RW -R (or -RW) it can only read other disks that are -R (or -RW).

The -R format has kind of fallen by the wayside because the +R is so much more 'universal'. But there are many many burners out there that write and read only -R.

I hope this helps answer your questions!