> Two of the bleeder screws were rounded in the process. I used a flare
> nut wrench specifically designed for softer fasteners.

Common problem with 'cheap' flare nut wrenches. Vice-grip makes a nice
v-groove wrench for just this job that will not round out a fastener.
Just an FYI if you have to do this job again.

> One of these rounded screws was apparently not tight enough. I
> discovered it was leaking. I capped off the bleeder screw with a small
> plastic cap and hose clamp. Today I plan on buying new bleeder screws
> and installing them.

Good.

> 1) Will I have to re-bleed all the wheels?

If all of the fluid leaked out of the system, then yes. And yes to your
2nd question too, if the master cylinder reservoir completely emptied
out then you need to bleed the WHOLE system. If all you had was a leak
at one wheel and you capped it off before it drained the system, then
you probably don't need to bleed any of the wheels except the one that
was leaking, and even at the leaking wheel you won't need to bleed it
very much. Put the new screw in, bleed it once and if you don't see any
air then tighten it up and forget about it.

Good luck with it.

Chris