Can I use PC3200/2700 DDR memory module in place of DDR266/PC2100 module?

Answer 1

Yes.
It may run at slower than native speed, however, it should work.

regards,
Philip T

Answer 2

I can not say for certain.
You may want to check with your computer support.
One sounds Laptop and the other Desktop (SODIMM/DIMM)? Check number of pins?
I have used some off RAM in an old Desktop and it did work, but, that no promise yours will. The main concern I had was the newer slowing down for what the old computer called for in speed.