Are you saying we cant get a bunch of spiders together to produce spiderweb armor? Crazy talk...
There
are spider "milk farms" that specialize on "milking" spiders! Problem is though that the process is relatively slow and requires
a lot of spiders. They basically strap a bunch of spiders to a bracket, inject a chemical which creates a continuous "want" to produce web, strap the first centimetre or so to a spool, and start winding!
Note:
I think that the chemical actually weakens the web a little... unless I recall falsely. And each spider produces next to zero pure solid webmass.
The web is used where it's wanted, such as in some beauty creams and so on. (Of course, not the web in its solid form! That would result in Ms. Munster I guess

)
Blunt trauma from a high caliber bullet would likely kill you anyway if you wore that stuff. As with traditional kevlar vests, you'll still want a rigid plate behind it to dissipate kinetic energy over a wider area.
Correct in both areas.
As for the high calibre bullet, small calibre bullets fired from e.g. sniper rifles would also cause severe trauma despite the very strong material.
Smaller bullets usually mean (but
not by default) a smaller tip = pretty high pressure. Also, energy is increased by a square factor depending on velocity, rather than on the linear increase depending on mass (mv^2/2). A bullet twice as light as a heavy bullet, travelling twice as fast as a heavy bullet, will cause
double the kinetic energy.
As for man-made materials, we do have some pretty serious stuff like graphene concepts and uranium tank-shell heads.