I grew up in Europe (Spain), where the term 'liberal' is understood as being centrist and pro-capitalism. You can be either a 'liberal conservative' if you lean slightly right, or a 'leftish liberal' if you agree with some socialist principles.
Here in the US, 'liberal' has a different connotation and it's often meant as 'leftist'. Something similar occurs with the term 'libertarian', which outside the US means 'anarquist'.
So, can one be a progressive democrat? I think yes, our political ideas don't need to be constrained within a rigid frame.

In a U.S context 'Liberal' is usually indicative of someone who is socially libertarian and fiscally centrist. Given the policies other industrialized nations, this is a less and less progressive ideology.

No

no...liberals still have themselves on the front of their minds. progressives have everyone's benefit on the fore front of their minds.

Less & Less these days.