I will try to answer you with the information I have :).
1. Rovinieta is valid for 30 days, not 2 weeks. Price: 7 EUR, about 30 RON. And is not necessary for caravan, only for the car. You can buuy it form the border, when you enter in Romania. Find a Petrom fuel station and ask about it. They will ask you for the registration document of the car to take the technical data and they will give you the rovinieta with a proof of payment. Keep that, as the rovinieta is valid only with that payment proof.
2. In my opinion the better is Brasov, Ploiesti, Bucuresti (don't enter in Bucuresti, from Otopeni turn left and keep the road until indication A2- Constanta). After you exit from A2, in order to avoid the congestion from Constanta, you can take a "detour" route: Poarta Alba - Nazarcea - enter in DN2A/E60 - after few km turn left to Tulcea and then to the right to Lumina. Keep the road and you will end in Navodari. You cross Navodari and go to those camping between Navodari and Mamaia. If you need more detalis, just let me know. The road is good and, as I already told, you will avoid the traffic congestion between Constanta and Mamaia and the local tax (as far as I know the tax is for every entrance).
3. In Navodari the access is free, but at Mamaia-Constanta I don't know what will be the tax this year. Maybe another colleague from Constanta will help you.
4. Yes, the highways in Romania are still free.
If you need more info, just write :).
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