Does Romanian have formal and informal speech? Like if you were to speak to friends vs a stranger.

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Yes. There are also different nuances. Youngsters have a certain jargon that they wouldn't use when addressing their teachers. Men who come out of the army service have a very colorful language (to put it mildly). Also some men, even with advanced degrees, tend to use some savory expressions when they talk among themselves that they wouldn't use in front of women. Of course, it's not universal, there are exceptions, but there is a trend.

Yes , there is formal speach but not so strict like in other countries because people are friendly . You are expected to be polite to a customer, your boss and pretty much anybody you don’t know personally (except, typically, people younger than ~25–30) .People are addressed by "Domnul" for Mr. and "Doamna" for Mrs., and their surname.
Romanian has a number of polite, formal pronouns The most important one meaning “you” is dumneavoastră, which is used instead of tu (singular) and voi (plural) when the circumstances require it. Dumneavoastră always takes the second person plural verb form ( even when it replaces tu used to address one person).