1. Logged in as a member (newbie), and editing the Profile you have the option of adding a UserHomepage. After saving the Profile, the Homepage appears as a link to :
http://www.mysite.com/userhomepage I am not sure what your trying to do but you need to put a full valid url in that entry. So for example my homepage might be....
PhotoPost PHP Photo Sharing Gallery with vBulletin Forum Integration
Hope that clarifies that
2. OK. Is it possible to have such features custom implemented by you and how much would that cost?
Honestly could not begin to say. You can send emails to chuck at photopost dot com but you would need to specify exactly what your after or more directly how your expecting things to work. Quotes can not be given without fully understanding those variables and estimating what time it would take. Custom work is done at the rate of $70/hr.
3. The user image (avatar) shows ok in SMF forum Profile but is a missing image symbol in PP Profile. How can I make it to show? See attached snaps.
Right click the missing avatar image what is the path? That itself will tell you without fail what your issue is. Most likely a wrong forum path. Without a link to your site we can not assist so we need to see the site. 
4. There is no such option in SMF forum admin. The membergroups are set based on posting activity. I want to "upgrade" a user to a membergroup with more privileges in PP (not in SMF forum). Is that possible?
You just need to create some special group in the forum and move people there. User management is done within your forum because thats where your users come from. There are no real users in photopost because your integrated with the forum user table. After you move people in the forum to some special group you can go to your gallery admin click on edit usergroups do a resync usergroups thing to grab the new usergroup and then apply permissions as you wish.
5. OK. Is it possible to have such features custom implemented by you and how much would that cost?
See reply above previously sounds to me like your looking for extensive usergroup settings being modified
6. I see the picture opening in its own window and not within lightbox (when the image is greater than the admin set size limits).
The thresholds you set mean that to use lightbox the image must be under certain dimensions. Thus if it is over that then it uses the regular big popupwindow. So in your show photo options in admin try upping your max lightbox sizes to 1500 from the default 900. You might need restrict your max image sizes as well. Lightbox is not meant to show 2500x2500 images with that there java code.