From the news coverage I've heard, the lockdown is implied to be voluntary- the authorities are asking
people to stay in their homes, not telling them that they will be arrested if they leave.
However, the situation is rapidly evolving, and I'm sure a better assessment will be possible once everything calms down.
Has martial law been declared?... I just Wiki'd Martial Law, and I'm not sure this situation would fall under the definition.
I don't think it has been declared; see above.
FWIW local authorities have declared martial law several times in American history, notably after the SF earthquake of 1906, but in most cases, modern scholars consider the legality of these declarations to be suspect or even outright groundless.