To start answering your questions:
Black Sea is not a warm water (but considering you come from Norway, you should be fine). Usually a 7mm wetsuit is enough. The visibility is not that great - 3-5 meters is usually good, 6-7 would mean you are lucky. Could be as worse as 0.5-1 meter. Diving from shore, you will find either sand or rocky bottom, the rocky one being more interesting. The sea life is poor: small stingrays, turbots, frog fishes, sea horses, rapana snails, lots of mussels, some jelly fishes, and a few other fishes. A good place to start is the small beach on the right of the Casino in Constanta - a nice shore dive, with 6-7 meters depth. You may see there old anchors, antique ceramics, and the antique greek harbour wall. In the same area (but you will need a boat) you may find some shipwrecks. There are other places also, but you should rather find a local guide at least for the start.
Places to get equipment&guides, in no particular order:
Bine ati venit pe DivingDelphi.ro (in Constanta)
Aquarius dive center - Constanta (in Constanta, near the Casino)
Scufundari in Romania, epave in Marea Neagra, scufundari de agrement, scufundari in pestera Isverna - ScubaDiver.ro CENTER (located in Bucharest, but coming to Eforie in weekends)
CARPATICA DIVE CENTER - HOME (located in Eforie, in the yachts harbour), usually available even on Sunday for air fills, specially if you call first)
To get a better idea of the diving locations, you may use this map:
Locuri de scufundare pe litoralul românesc
let me know if you need any comment translated (they are in Romanian)
Usually the rental equipment will be Coltri, Seac, Seemann; most probably not top brands like Scubapro, Aqualung, Atomic and so on. So if you have a good regulator or BC, bring it with you. Rental price should be something like 20 Euro/day, excluding the air fill. A 15 liters air fill to 200 atm will be ~6.5-7 EUR. The equipment is usually well mantained, including the compressors.
Local laws forbid any means of hunting underwater if you are into this, so just skip it as long as you are in Romania.
What else should I tell you about this subject?
