"Que" is a conjunction that introduces subordinate clauses and cannot be omitted in Spanish. These syntactic units(adverbial particles) need to rely on previous context in order to be understood and interpreted. E.g. Q: ¿Estuvo con nosotros? A: Sí, me parece que sí/creo que sí, eso creo, hmmm sí estuvo (=I think he/she was). Unlike Spanish, English would overtly express the subject. ¿Es puntual? Supongo que sí(=I guess probably she did)
- Q: ¿Van a venir? A: Yo no.(Q: Are you coming? A: I don’t.)
English would use auxiliary verbs instead.
- Q: ¿Hay fiesta? A: Parece./Parece que sí.(Q: Is it a party? A: I think so/I think it is)
Some authors use either the term "adverbial particle" (with syntactic independence) or "polar adverb" (providing positive or negative polarity to the sentence). Anyway, this happens in both languages, "so" doesn't mean anything to me it must be interpreted either positively or negatively, it will depend only on the previous context on which it supports itself.
"No hay de qué" is like saying there’s nothing to thank me for(Don't mention it) Some people say it's dequeism, that is, the inclusion of the preposition "de" is a subordinate phrase normally introduced by the conjunctive pronoun "que" alone.
"Y a mí qué" (What's that got to do with me?) this situation has nothing to do with me.
- "¡Ay de ti si ..." (if-clause) woe to you if/ If you do/don't you'll regret it.
¡ay de ti!
( ¡ay de ustedes!)
1 Expresión con que se amenaza a alguien si no cumple o hace lo que se le pide. ¡ay de vosotros si me desobedecéis!
- "Sabe donde está, pero hace como que no" (=he/she pretends not to./He/She's pretending not to.)(in order not to be redundant)
The following was stated in the previous sentence, but ending a sentence with a preposition is usually considered grammatically incorrect. E.g. It's better not to. You would have been a fool not to.