I've seen documents and a VIN plate of a crashed German Caterham on ebay.de... It went for €600 or so... I've read people do the same in the UK -- buy the identity of some old Dutton and stick it on their newly built kit car. Most likely illegal, but could work.
What some people do here in Lithuania is register self-builds as self-built tractors. They are regulated, certified and registered by a different agency (~county's department of agriculture), so it's a lot easier (but then you have tractor number plate on the back with green lettering, no plate in the front, and formally you're not allowed on motorways and can't exceed 40 km/h, he he). Ask around, that may be possible in Romania, too.
For applying a VIN to your car, yes, you need to buy a set of number/letter punches, and punch it on a 3 mm plate which you then weld onto a chassis member (there are some guidelines for positioning it in the IVA manual).
I'll repeat for the n-th time: consider registering in Poland! They have lots of kit cars and self-builds (have a look at the galleries in
http://www.lotus7.pl/galeria/), a much laxer approval procedure than in UK, several companies specialising in kit cars (though I didn't have much luck trying to contact them by email).
http://walenda-motorsport.pl/ ,
http://www.t-c.pl/kit-car-en/#/HOME