When I install CS5.5 (upgrade) in a new computer , it says that there is no old version in the computer. I have older versions CS3 and 1.1 do I have to install them also?

no.

but after entering your cs5.5 serial number, the installer will search your computer for cs3.  failing to find it the installer will present a dropdown of previous versions.  select cs3.  you will the be prompted to enter the cs3 serial number.

enter the correct number at the correct time and installation will proceed.