Does CD-ROM allow you to read write and erase?

In general, no. CD-ROM is read-only. You can only read from it after a manufacturer writes to the disc permanently.

However, there are recordable CDs (CD-R), which allow you to write once.

And, there are rewritable (CD-RW), which allow you to write and erase many times.

The same goes for existing DVD technology (DVD, DVD-R, DVD-RW).