1.) Yes, better to hit the uphills harder. But it's pretty unnatural to do anything other than riding hard up the hills and easing up on downhills.

2.) For maximum speed, you should stay in the drops except when climbing (going up a hill that's steep enough to drop your speed a lot), generally.

At the same power, a person in the drops is going to go faster because they are more aerodynamic.

The point to notice is that if you sit up, you are generally capable of producing more power. This is why people sit up on climbs. The added available power is enough that you'll go faster, even with the added aerodynamic drag.

Since you seem to be interested. It's worth noting that in power on the flats goes up with velocity cubed, while power on hills goes up directly with velocity. This means that if you want to go twice as fast on a slow climb, you must produce twice as much power. If you want to go twice as fast on a flat road, you need to produce 8 times as much power.

here is something a starter rider should focus on.
feet..pedals.
hands..handlebars.
arse..saddle.
and pedal.
waste time with power issues when you are contesting races.
for now just enjoy the ride. life is better when simple.

"Life is better when simple." Bingo!

Goodness I need to start going through these threads sooner.
I work on perceived airspeed. You might call it relative wind or effective wind. You might think I'm an idiot, but apparently I'm good enough to do aero analysis for a certain European pro team periodically. What do you do?

too not to