Upgrade 7.01.06 to 7.02.07 keeping sessions

You will have to tinker some, really can´t remember in the back of my head of what was done.

Thats not going to work.
7.02.xx uses classes for authentication and 7.01.06 uses procedural code

I think you could better spend your time in making the authentication with cookies working on your webhost. Almost every PHP Application with authentication uses cookies. I cannot image your webhost can not get it working.
Also advertising websites uses cookies, webshops etc.
If it does not work on your host, then my advice would be search for another host.
Also: Cookies are stored on your local computer not on the server.
Are you very shure the settings of sitepath etc are correct in you Fusion installation?
It can make difference to put www. in front of or not.

Edit: Blue Host offers Wordpress Installation. Don't they use cookies?

Believe me I have been working with networking problems and different hosts for a long time now. I have never encountered anything quite like this before and yes; Blue Host defaults to Wordpress when you buy a hosting package which uses cookies. That is what's so strange. I tried changing my 7.01.06 to use cookies, deleted the db table 'sessions' entries, deleted the 'host server' session files, deleted the cache and cookies on my local computer and it STILL won't work. I guess I'll open a ticket with my host and go from there and thanks for reminding about the 'class authentication' with 7.02 ... you're right; my idea won't work.

One thing you can check with chrome browser debug tool you could check if the cookie with the name "user" is beeing created on your computer when logged into fusion

Yeah I'll try that. But also my main whisperwillow site still uses 7.01.06 and I've never really had a problem with it. I'm gonna keep my new site 'trans-galactic.com' at that level too at least for now. Thanks for your help. :)

I also had problems with login on PF 7.02.07. Tested cookie "user" not beeing created. Tried different browsers, different PC, clear cookies, checked sitehost settings etc. No succes until in Cpanel switched from PHP 5,6 native to PHP not beeing native and problem was solved.