Those are really good questions, which show that you are trying to engage seriously with the underlying concepts rather than simply apply formulae mindlessly. Having said that, at GCSE or even A Level, you can probably get away with a bit of rote learning at first while developing a deeper understanding of the concepts, so don't let this hold you back too much.
Your two questions are actually related. You are right that all waves need "particles" (more generally described as a "medium") in which to move (or "propagate"). This is true even for light, although the medium there is rather a special one which has no absolute reference frame (which is another story...).
For sound waves, the medium is usually air (but in general it could be any solid, liquid or gas), which is a collection of molecules moving around at high speeds with very low density. For a wave to propagate (move), energy has to be transferred from one group of molecules to the next. This is very difficult to do by transverse motion, because the viscosity of air is very low. Try to extinguish a candle by moving your hand up and down next to it (without pushing air towards it) - you will have a hard time.
On the other hand, air exerts a non-negligible pressure by virtue of the fact that the molecules are moving at high speeds. Air can be pushed from one place to another, and it has a certain 'elasticity', like a solid, but only when it is confined or pushed at high speeds. This is why it can support a longitudinal wave. Try to extinguish a candle by pushing air towards it, either by waving your hand or blowing - it's quite easy to do.
In contrast to gases and liquids (which are both fluids), sound waves in solids CAN be transverse. This is because atoms in solids are usually bonded together by strong forces, and their viscosity is extremely high (effectively infinite) compared with fluids. Earthquakes, for example, have longitudinal and transverse components which arrive at different times, and can transmit huge amounts of energy. The energy is transferred by the fact that one part of the solid is rigidly connected to another in a way that couples both lateral and longitudinal motion of the atoms.
You may wonder why light is a transverse wave and not a longitudinal one. That is an excellent question, but unfortunately a full answer goes well beyond school physics into something called Maxwell's equations. Suffice to say that electromagnetic waves do not behave like matter waves, and there is no easy mechanical analogy to explain how they propagate.
That was probably far more than you wanted to know, but I thought the questions were interesting.