Thanks for the thought provoking questions Doane.
Is mankind doomed?
In the broad sense that mankind shall one day become extinct, or perhaps evolve to such a degree that we may as well be considered a new life form, then my answer is; very likely yes.
In the short term, I expect we will continue to exercise our ubiquitous human cleverness in solving the technical problems required for survival. However our population in the near future will likely fluxuate wildly unless we master an increased degree of reason, tolerance, and benevolence. Our survival in the short term will depend upon both our moral behavior as well as our technological solutions. Be also mindful that it is believed that over 99% of the species which have existed on this planet have by now become extinct. We are here without a safety net beneath us. Our short term survival is for all practical purposes, entirely in our own hands
In the very long term the odds are against our continued survival. An analogy was given by Richard Dawkins in his book
The Blind Watchmaker;
"If we...lived for a million years...we should not make a habit of crossing roads...for if you crossed a road everyday for half a million years you would undoubtedly be run over".
Survival in the very long term runs afoul of statistics. It may be a killer asteroid, or perhaps a variation in the sun's energy output that will end our world. We might escape in an intergalactic spaceship before the first axe falls, though it is clear that life is cautiously treading forever through a vast minefield. Given the length of the minefield, our caution pales as compared with the patience and number of the mines.
Are we evolving philosophically?
My answer is both yes and no. Unfortunately, humanity enmasse never has taken to heart Socrates assertion that, "The unexamined life is not worth living". Our philosophical evolution appears to result more from the works of isolated thinkers of great stature. This is in contrast to the technical fields in which steady advances result from the combined efforts of the masses.
While the understanding of Euler and Einstein was more complete than that of Archemedes and Newton, it is difficult to characterize the music of Mozart as superior to the earlier Bach, or the philosophy of Sartre as superior to that of Schopenhauer. To quote Andre Comte-Sponville in his book titled,
A Small Treatise On The Great Virtues,
"Science lives in the present and is always forgetting its first steps. Philosophy, to the contrary, is always trying to retrace its first steps and has been from the very beginning. What physicist rereads Newton? What philosopher does not reread Aristotle? Science progresses and forgets,; philosophy ponders and recalls".
Thus, progress in philosophy comes in fits and starts, occasionally appearing to be in retrogression.
To move from the exceptional intellectual to the average man-on-the-street; Is the aesthetic sensibility of an average mall shopper today improved upon that of his or her direct ancestor, perhaps a European agrarian peasant of the Middle Ages? Successively consider both descendent and ancestor their ethics, metaphysics, and epistemology.
I do not believe the average mall shopper has an improved aesthetic appreciation over that of the earlier peasant. (another thread perhaps

)
Despite the horrors of the 20th century, I do believe that the sense of ethics among the masses is improving, albeit painfully slowly.
Despite the continued and widespread belief of the religious superstitions of the past, the vast number of irrefutable scientific successes has made inroads. A crack has formed in the once sound monolithic support of religious dogma among the masses.
The above observation applies equally well to epistemology.
Do we live by our beliefs?
My answer is a simple and unequivocal yes. Humans have always done exactly so. However, the actions of a man of few personal beliefs will often appear to us with strong beliefs to be random and amoral.
Thanks,
Michael