Can I carry my folding bike by using the rack as a handle? I put a new rack on this bike. The rack says it can hold up to 25 kg which is about 50 pounds. Can I use this rack to grab it and carry it while it is folded? The bike is about 35 pounds. 

Or this way (holding the crank?)? In this position, it rests on the frame.
You probably would be alright. But just take into account that the 50 pound carrying limit is for your rack and what it can carry, not the four screws that attached the rack to your bike and what they can carry. 

In essence, it would be like taking a 4000 pound winch, securing it to a high position, and lifting an f250 into the air with it. The winch itself would probably be ok, but the mounting area where you attached it to the vehicle would probably fail. 

I would suggest being very careful if you choose to carry your bike by the rack. Personally, I would find a grip on the actual frame itself.

Hope this helped!