1 - Can this situation be boiled down to lifestyle choices? How?I imagine they play a part, but I don't imagine it would be a very big part, and I can't think of any way to boil "it" down to make it fit the idea that people's social mobility is
solely their own responsibility.
2 - What would you specifically point to the problem being - what is the biggest hurdle?The perception that social mobility in the general US population is very large in the first place - it isn't. The biggest indicator of the peak social status of any random American is not intelligence or ability or application (or race, for that matter, though this probably still plays a bigger part than the first three); it is the peak social status of one's parents. This is also largely true here in the UK (and we've still got an aristocracy to use as an excuse - what's yours?

)
The Horatio Alger
myth is just that.
Now, in a capitalist economy of almost 300 million people it's going to be really easy to find enough people who have managed to buck the system to confirm that social mobiliy is alive and well and that anyone can do or have anything they want provided they work hard enough. That's not the picture of a mobile society, that's confirmation bias.
Why? Because we all know people who work really hard and haven't clawed their way up to be CEO/movie star/billionaire/whatever. You can't get that kind of success
without working hard (unless your folks did, eh Paris?) but success does not automatically follow from hard work.
Someone once said that success is the point where hard work coincides with opportunity (for which read luck - and only lucky people believe that they make their own). My point is that you need BOTH, and in a society where the poor generally are marginalised and excluded, opportunities are just that little bit scarcer for the poor than for everyone else. And, where disproportionate numbers of poor people are black, black people are disproportionately less likely to succeed.
Parenting must play the part, but if the entire black population of North America got married for life tomorrow and raised a whole decent honest crime-free children to mature hard-working welfare-shy adulthood ('cos none of that happens today, of course

) American would be no more of a mobile society in 20 years than it is now. (That is, if that's the ONLY thing that changed.)
3 - What can be said about the decline of economic well-being for black men? Why has it declined in the last 30 years when many economic indicators have risen?I'm guessing, but I'd say that the economic well-being of the numeric majority of black men 20 or 30 years ago was more likely to be driven by the old-style manufacturing industry that has mostly been outsourced these days. Ghettoisation has meant that new replacement industries (e.g. IT, finance, service sector generally) have been slow to come into predominantly poor blue-collar areas across the board (black and white - are the mostly white coal-mining or steel-making areas of, say, Pennsylvania better or worse off than 30 years ago?).
So unskilled and semi-skilled labour, of which black men were disproportionately part (for many reasons, not limited to but including dysfunctional families and - where did that elephant come from? -
racism! Gasp! I said it!) has been hit hardest by the shift towards a "knowledge economy" from a manufacturing one.
QED.
Ok, maybe not, but there must be some element of truth here.