No. The top gear will likely already be at the maximum the engine can cope
with. Taller gears than this will likely result in slower, not faster
speeds.

As Mark indicated the maximum speed will be limited by the power of the
engine, the design the body and the final gearing ratio.  Simply
gearing the drive train up will probably result in a slower top speed.

Imagine riding a 16 speed bicycle.  In high gear front and rear you
might be able to crank out 25mph depending on your legs.  If you
increase the gearing to the bike covers an even greater theoretical
distance for every turn of the pedals, but you the rider have to push a
lot harder.  Chances are your speed slow down.  Same principle applies
to a car.

No. Top speed is limited by available horsepower, which doesn't change
with what gear you are in.

Gearing allows you to keep the engine close to its best operating speed
at the different road speeds it will encounter from just faster than
stopped all the way up to its maximum operating speed. But the highest
gear is typically chosen so that maximum engine power coincides with the
speed at which total power required by drag is equalled.

A higher gear than that would make the engine run slower and produce
less power than it was producing in the old top gear and so the car
would slow down. Some cars actually have their highest gear setup like
that so that the engine will be turning slower at highway speeds.

All more gears would do for you is keep the engine closer to maximum
power as you accelerate, letting you get to top speed a little faster;
at least until you have so many gears that the time spent out of gear
while changing eats up all the advantage you've gained.

Generally not.  Most cars -- and certainly just about anything with a
1 liter engine -- are "drag limited" in their highest gear --
that is, their top speed is lower than the speed that would be
achieved at red-line in top gear.  Gears higher than that would have
an even lower top speed.

Not necessarily.  You eventually have to deal with wind resistance at
greater speeds, and that's the major factor in preventing a vehicle
from going any faster.

Define substantially.  If the gears 6-15 are spaced evenly like the gears
1-5 are, gear 6 might be useful.  Much beyond 6, there wouldn't be enough
horsepower for the engine to turn over.  (likely, the engine would stall)
Another problem is, the tranny would be much heavier, meaning that the
engine would need more horsepower to go the SAME speed.

I think you'd be lucky to raise the top end speed by 10MPH or so.  -Dave