Hello Priscilla, I'm a newbie around here but I'm happy to respond you as best as I can. Note that my advices and answers has no professional qualifications, but I will try to answer as close to reality as possible.
Prices may vary very much in Cluj-Napoca, for start lets talk about the Center of the City, the most wanted because... as any city,there's action. There are many people who'd like to be close to their most frequent sites, for example foreign students, want to be near Universities and most of them are in the center of the city,also the ones that are trying to avoid the rush hours are eager to live in the center. morning and afternoon working hours can be stressful, it wasn't always like this but its still in its course of development so its just natural . Prices for rent in the center of Cluj-Napoca are between 7-15 euros per square meter depending on location and the endowments. Cluj-Napoca it is a very friendly City,people are peaceful and calm...Recently Grigorescu district was voted to be the safest place to live in Romania, rents are between 5-10 euros per square meter,Zorilor is the next district most wanted,prices are a bit higher in Zorilor district,(you can have beautiful views over the city from Zorilor,its a rocky hill . ) and recently Marasti district shows very much interest (the one with Iulius Mall ). The most affortable are in Manastur district on the west side of the city. Gheorgheni district acts mostly like Marasti, but I'm guessing its a bit peaceful. Not that are gangsters in the rest of the districts ). but it a district mostly with elder people, so if you are planning to move in there, not so much a good idea if you are a bit noisy. Joking . They are very nice and kind people. This is a feature here in this part of Romania, everyone is calm and kind,well not everyone but most of us are.
Aside from Cluj-Napoca districts, there are also vecinities, like Floresti and Apahida which has good prices for rents ,I'd say between 4-7 on average Euros per square meter.
The prices for buying a flat or a house is harder to determinate,but there are somehow proportional with prices for rents but much more higher. For example: a square meter can be above 1000 Euros/meter square ,on average for the most parts,with slightly differences. I currently live in Marasti district, I lived my childhood to Zorilor. I might move back to Zorilor someday. I recommend any of them.
About Real Estate policies, my personal thought is that are best to be avoided, they just put themselves between the transactions for an extra fee which is to be paid either by client or owner or both , you can reason with individual parts. Legal contracts can be made with individuals.There can also be translated and signed by both sides and they are legal.
I have a bad experience with a Real Estate while trying to purchase an apartment,so its a BIG NO for me.
Property taxes and fees are according to the usable surface,I don't know so many details but details can be given from an legal office of property taxes and fees.
Hope its good enough. Best wishes! Any further questions are welcome!
Bun venit in Cluj-Napoca