The effects are similar, but apart from torque you also have other aerodynamic factors at work. Torque is mostly about two parts joined by a common axis, when one things turns left (for example the propeller), the other one wants to turn right (the fuselage, which means the wing opposite the prop's direction is dipping lower). This is clearly on the roll axis.
As for the sideways pull, that is on the yaw axis of motion.
The propeller's rotation creates a swirling mass of air that travels along the aircraft's fuselage. This swirling air usually hits one side of the tail more than it does the other.
Imagine having spray paint injected in front of the propeller to observe this, you would see a corckscrew shaped pattern travel from the propeller backwards and depending on the dynamics of it all (eg, propeller RPM, propeller blade shape, fuselage length etc), most of the paint along this corckscrew would hit on one side of your tail.
This effectively means that the vertical part of the tail functions like a "sail" against this mass of wind, moving your tails sideways (and turning your nose the other way as a result). I think this is called p-factor, someone correct me if it's not. This is a simplistic explanation strictly from memory, but googling about p-factor you'll be able to learn more.
The reason it's better to apply throttle smoothly during take-off has to do with this effect and the way the control surfaces work. If you hold your brakes while pushing the throttles to full, you have the maximum amount of swirling air hitting the side of your tail to fight against, but you have no forward motion whatsoever to create an airflow over your control surfaces, which means ineffective controls to fight it with.
However, if you only apply 30-50% of throttle you greatly reduce the yaw motion induced by this effect. Also, when your plane is steadily rolling along the runway your forward motion creates a relative motion of air over the control surfaces that makes them effective. So, you apply throttle about mid-way and as soon as you're moving at 50-100km/h (30-60mph) or so depending on aircraft type you can advance your throttle the rest of the way and be sure you have enough control authority to counteract the sideways pull.
There's even more dynamics into play here of course. For example, tail dragger planes rely heavily on short bursts of power to create airflow over the tail surfaces in an effort to help with ground maneuvering and taxing.
The trick here is that these are brief actions and the sideways pull doesn't have enough time to manifest. You can almost turn on the spot by applying brakes only on the wheel inside the turn ( that is, left wheel for left turn and vice versa), kick the rudder into the turn and briefly apply some throttle (or a lot of it, experiment and watch the results). The plane doesn't have enough "power on" time to start accelerating and veering all over the place, but the sudden burst of power and increase in propeller rotations creates a "block" of moving air mass that crashes into your deflected rudders and helps you turn on the spot, without having to get the plane rolling forward first.
You don't really need to fret about memorizing exact sequences of actions to perform.
The important thing is to just know that these effects are there and
observe how they affect your flying. Different aircraft have different behaviours and even the same plane behaves differently depending on its weight/load-out, power settings (throttle, etc), even weather conditions.
Best thing you can do is jump in an aircraft you like (preferrably early war, since they are lighter, easier to control and have less powerful engines and thus less available torque) and run a sequence of test flights to get a feel for it. Just fire up a mission in the quick mission builder with no enemies around, go to the airfield and start practicing take-offs/landing/touch and go sequences a few times. When you are satisfied that you know how it works (it doesn't even have to be perfect, just non-lethal
), change something and observe the effects. For example, after getting comfortable with take offs using a gradual throttle input, try the same thing with abrupt throttle inputs, then with something in-between and so on. Chances are that within 5 attempts you will find the "sweet spot" between doing things fast enough but not so fast that your plane runs away under you.