How much are the buses? How long do they take?
Which taxis are "safe" to take from the airport? How much should they be (to Piata Unirii)?
Also, how much is a taxi from Piata Unirii to the Ghencea?
The buses are 3.5 lei I think (7 lei for the return trip), and they take around half an hour, depending on traffic.
At Otopeni there are only taxis from a company called Fly Taxi, they have an exclusive deal with the airport, but they're expensive (3.5 lei / km - while most other companies are 1.2-1.6 lei / km). So with Fly Taxi, you should pay around 70-80 lei to downtown. Also - always make sure the meter is running. Even if it's a big company, they won't have any issues trying to rip off foreigners.
From Piata Unirii you can find tons of normal priced taxis, a trip to Ghencea should be around 15 lei (~3 GBP). Make sure the price displayed on the taxi is 1.2-1.6 lei / km, anything more expensive is a rip-off.