About team's following and popularity, see
here.
Yes, Steaua is the most popular club in Romania. National has a very small fan base. There are rumours of them merging with Universitatea Craiova - a very popular team. Universitatea is the last team (outside of the capital Bucharest) to win the championship in 1990/1991. Unfortunately, they're now at the bottom of the table.

Disastrous management...
Transfers to big leagues. Well, almost any league from Europe is bigger than "Divizia A", so I guess a move to Ukraine is to be considered a move to a big league.

So, there you go: Cristi Irimia (right back from Dinamo Bucharest) moved to Dinamo Kiev.
Other rumours: Mihaita Plesan (central midfielder from Universitatea Craiova) is wanted by Steaua Bucharest, Galatasaray Istanbul, Besiktas Istanbul, Ajax Amsterdam and Deportivo La Coruna. Also, many players from Dinamo Bucharest have offers from Ukraine and Russia. Oh, and the top scorer - Daniel Niculae (Rapid) is wanted by Shakhtar Donetk.
About that stadium. I guess it's "Giulesti" - Rapid's stadium. But as I don't live in Bucharest, I can't be sure.