Learn French: Est-ce que c'est celui avec qui tu as eu un rendez-vous ?

In French, you can never end a sentence or a clause with a preposition. A preposition like avec (with) must always come immediately before the relative pronoun it links to. So, instead of saying 'who you had a date with', you have to structure it as avec qui (with whom).

Could I use avec lequel or avec que here instead of avec qui?

You cannot use avec que, because the relative pronoun que is never used after prepositions. You could technically say avec lequel, but when referring to a person, it is much more natural and common to use avec qui. Lequel and its forms (laquelle, etc.) are generally reserved for referring to things or animals.

Why do we use celui in this sentence?

Celui is a demonstrative pronoun that translates to 'the one' (masculine singular). We use it here to refer back to a person without repeating a noun (like 'the man' or 'the guy'). Since the context implies a male ('Is he the one...'), we use the masculine celui rather than the feminine celle.

Does un rendez-vous always mean a romantic date?

Not necessarily! While un rendez-vous can mean a romantic date, it is also the standard French word for any kind of scheduled appointment (like going to the doctor or the hairdresser) or a professional meeting. You always have to rely on the context to know which type of meeting it is.