oh, man, i'm so glad no one's angry on me because of 
posting the same problem again.

i have tried to rename any project's folder AND it's .whtt 
file and i have to say that it hasn't influenced the links 
stored in available projects index.html - which means that 
old names of projects were on that list, and not the new 
one... but as i remember, i have tried that before, when i 
have had installed previous versions of HTTrack, and 
everything was ok - all new projects names were on that 
list, which is IMHO normal for index.html to automatically 
update changes that i have made. (or maybe i'm wrong?)

one more thing - when i have had installed HTTrack v3.20RC3 
via installer (.exe version) and run it, there was 
two 'strange' things: there was no 'ftp via proxy' window 
pop up, in which i have to set a proxy for program to use 
while d/l something via ftp; second strange stuff is that 
on a main HTTrack window (where i'm asked to enter the name 
of a new project or to choose the old one) in a 'base 
path:' field it stays the path to the folder in which all 
my projects r stored (because all my projects r stored in 
one folder)... but when i install HTTrack via .zip file, 
there is a pop up window and in a 'base path:' field it 
stays 'C:\My Web Sites' path (which is normal for me to see 
that, because it was the case with previous versions)... 
but i do not know if this is something important...