Si tú supieras lo que te he esperado
I'm afraid "If you knew that I've been waiting for you" isn't a good translation. "Lo" in "lo que" is the article used when the following noun is omitted:
- El aspecto más interesante = lo más interesante
I omitted "aspecto" there because it didn't really add any meaning, and I did so by changing "el" to "lo". Generally, the word omitted isn't really anything, but just a meaningless pronoun:
- Lo que me gusta de ella es que es divertida = aquello que me gusta de ella es que es divertida
However, sometimes the word elided is a meaningful word, but one than can be perfectly understandable without making it explicit. The example at hand would be one of those cases:
Si tú supieras lo que te he esperado = si tú supieras el tiempo que te he esperado
(If you knew how much I've been waiting for you)
Note: In English, "wait" is intransitive (i.e., it can't take a DO), but in Spanish it can. You can say "estuve esperando dos horas", which would translate to "I've been waiting (for) two hours".
Si tú a mi lado vas a tener al que más te adora
Once again, the translation provided is not on point. A better translation would be "If you'll have by my side the one that adores you the most". The sentence is incomplete, I guess because it's lacking a context. "A" from "al" is necessary because in Spanish, both direct and indirect objects require "a" when the object is a person:
- "Vi una película." but "Vi a tu hermano."
The preposition is necessary when introducing a person, even though "al que más te adora" is a DO, which generally wouldn't be introduced by "a".
Y yo lo puedo ver, dime qué vas a hacer
You are right "qué" is a question word, just like "what" is. And here you have a question, but it's an indirect one:
- ¿A dónde vas? = Quiero saber a dónde vas // Dime a dónde vas
- ¿Qué vas a hacer? = Quiero saber qué vas a hacer // Dime qué vas a hacer
Btw, "Dime lo que vas a hacer" is just as fine as "Dime qué vas a hacer". Only in the former, "lo" would be standing for "aquello" (Dime aquello que vas a hacer), and "que" would be a mere linker without any semantic meaning, whereas "qué" in the latter would be a pronoun with full meaning.