HTupolev

If the aluminum-framed bike is lighter than the steel-framed bike, it should climb and accelerate better, although the weight shouldn't have much effect on how fast it rolls.

I say "if" because a bike being aluminum-framed is no guarantee of lightness. If you care about weight, check how heavy a bike actually is, don't just look at frame material. Frames are a minority of bicycle weight, and "steel versus aluminum" isn't a very precise check, because there are many steels and many aluminums, and various ways of constructing frames from them.

If you want to go fast on the road, posture is crucial. At high speeds, aerodynamics are a vast majority of the resistance a bicycle is fighting, and the rider produces the vast majority of aerodynamic drag. The single biggest reason that a top-end road bike is faster than a cheap hybrid doesn't have to do with it being high-end, it's the fact that it'll typically be fit so that the rider is low and aerodynamic, whereas cheap hybrids tend to hold the rider upright and non-aero.
You don't necessarily need to go crazy aggressive on the posture to get most of the benefits, though. Road touring bikes are usually significantly more upright than high-end racing bikes, but not horribly slow.

As far as the first "upgrade" to look into... tires. High-performance tires are a low cost of entry, and can make a tangible difference to a bike's liveliness and speed.

The other big thing to make sure of is that a bike has the gears you need. Spinning out your gearing on the high end is annoying, and bottoming out your gearing on a climb can destroy your performance.

BUT. Unless something about your bike is seriously messing you up, the really big thing is always what the rider is doing. Be strong, draft when appropriate, etc. There's no substitute for being a fast cyclist.

Yes.