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Question

Why: que había muchas opciones rather than: que hay muchas opciones or even subjunctively: que haya muchas opciones?

Accepted Answer

Hola Garry
The whole sentence is:

La chica de la oficina le respondió que había muchas opciones.
The girl from the office replied that there were many options.

The verb in the main clause is in the past tense "le respondió" so it makes sense to use the past tense in the clause: ...que había... to maintain both actions in the past. 
This is why we used "había" instead of the present "hay".
As for the use of the subjunctive "que haya" instead,  we are using a verb that is "declaring" something, seen as a fact, something that "does happen" (decir, responder, explicar...) - being a declarative verb you're going to find the indicative. Other examples using the indicative could be for example:

Mi padre dice que soy muy traviesa. (indicative)
My dad says I'm very naughty.
Me comunicaron que la empresa iba a cerrar pronto. (indicative)
They informed me that the company was going to shut down soon.
El profesor nos explicó que no era la fórmula correcta. (indicative)
The teacher explained to us that the formula wasn't correct.

I hope it clarified it.
Saludos
Inma