My best suggestion is to ignore everything about MyHeritage and concentrate on Geni if you want to stay,- they are "just" the owners of Geni, and as stated several times before: Geni will continue as before, but now with better resources and access to technology from MyHeritage (and hopefully the other way as well).
● http://help.geni.com/forums/21545466-things-to-know
Of course you can find your family lines on MyHeritage, - I have found at least three trees there with my family.
As with Geni MH are not building any trees, - the users are, and the reason why I find my family there is because someone in the my tree have exported a GEDCOM and uploaded it on MyHeritage (and several other places as well). You find the name and contact information of that person on the MH tree.
The main reason is that MyHeritage probably is the only site that imports GEDCOM's from Geni easily and are even able to download documents and images linked backed to on Geni in the GEDCOM file.
Most of these imports are probably done in the Family Tree Builder program you can download from MyHeritage and install on your PC, which is probably one of the better free software for genealogy you can find.
Unfortunately that program insist on uploading to MyHeritage as well after the GEDCOM import, and if you don't say no to that question your data will end on MyHeritage in addition to your PC.