I am under the impression that elements from the third period onwards can promote electrons into d orbitals to form hybridised orbitals. Why would an element in the third period promote an electron to the 3d orbital when we learn that 4s orbitals are filled first because they are lower in energy (is it to do with orbital penetration?) Why also can a 2nd period p block element not promote to 3s?
There is a considerable amount of debate as to whether d-orbitals of main group elements (I assume we’re talking about them here; the discussion is rather pointless for d-block elements) are used in hybridisation or not.
Originally, the octet expansion, a.k.a. using them, was postulated by Linus Pauling because he was unhappy to use charge separation to describe molecules such as sulphur trioxide. However, it is entirely possible to draw Lewis structures that do not violate the octet rule and hence do not require d-orbital hybridisation for practically every case. There may be more mesomery required in some cases and less in others.
I’m not too good at repeating the arguments of supporters of main group elements’ d-orbital hybridisation theory, because I belong to the other group. The main argument against d-orbital participation is, as you noticed, that they are far removed on an energy scale; even behind the next s-orbital (3s, 3p, 4s, 3d) — hence the order of elements in the periodic table. I also have troubles understanding why phosphorous would only allow one d-orbital to hybridise, sulphur two and chlorine and the heavier halogens three. This makes no sense to me. (It seems to make sense for others, though.)
In my opinion you are absolutely correct in asking that if a 3p-element can use 3d orbitals, why should it not use 4s for hybridisation, and consequently why 2p cannot use 3s. Assuming 3d orbitals to be used, I could not answer your question satisfactorily.