If the old software came with the old computer, in other words bundled with
it, that is OEM software and cannot be legally transferred to the new
computer. If this was software you purchased, depending upon the terms of
the EULA for that software, you can usually move it to a new system. You
would need to check your license for that software, the EULA, End User
Licensing Agreement, can usually be found somewhere on the install disk for
the software, sometimes it's called "EULA" and sometimes it's just called
License or Licensing Agreement.
As to Favorites, on your old computer, open Internet Explorer, go to File,
select Import and Export and follow the screens for exporting. Make not of
the location where you export this file, it will create an HTM file and will
contain all your favorites expressed as HTML links. Save this file to some
removable media, floppy, CD-RW, etc. move it to your new computer, copy the
file to a temp folder, open IE as above and follow the screens, this time
for Import. Once the process is complete, your favorites will be loaded on
to your new system.