That pretty thing is the Babich Leningrad built by Arkadij Dmitrievich Babich. It took 3 years to build in the mid-50's and was apparently Babich's third homemade car. Pretty impressive work. It was powered by a 3.5 liter GAZ-12 engine out of a limousine that made 90hp and could get it up to 80mph, which is mighty impressive for a Soviet car. Here's some footage of it driving around. Looks spirited.
Babich went on to design a light tubular sub-frame for the KVN 2500S race car which was one of the most successful cars on the Iron Curtain circuit which is why most of us have never heard of it.
UPDATE: I forgot to mention the Leningrad still exists and will apparently be restored some day.
Next we have the Hadi EP-900 which was based on the Zaz 966. It was built in the 70's and I can't find too much info about it in English, but it's rad. Maybe someone who speaks Russian can tell me what this guy's going on about.
UPDATE: From commenter Mjag comes this:
about yellow car, it was experimental car made by HADI - KhNADU - ( Kharkiv National Automobile and Highway University is a Ukrainian university in Kharkiv on the base of Zaz 966 with mix of parts from VAZ and Moskvich with tubed body-on-frame and fiberglass body shell so its not quite Homebuilt car.