Learn English – it is hurt (Simple Past) or it is hurting? In the next situation

The question at the end of that sentence sounds odd because you are mixing a plural noun (i.e., rooms) with a singular noun (factor) before the verb.

Consider:

Do illegal rooftop subletted rooms cause such tragedies?

In that wording, the plural rooms matches with the verb cause.

Or:

Is this the only factor that causes such tragedies?

In that form, the singular factor matches with the verb causes.

Your sentence mixes the plural rooms with the singular factor, making it hard for you to figure out which form the verb cause(s) should take. (This isn’t necessarily ungrammatical, but sometimes this can make a sentence sound odd.)

I think one easy way to remedy this is to use the noun form of cause:

Are illegal rooftop subletted rooms the only cause of such tragedies?

but you would have to decide if that shifts the meaning of the sentence too far away from your original intent. If so, you could try removing the that, and using an -ing form:

Are illegal rooftop subletted rooms the only factor causing such tragedies?

To found is correct: to set up or establish on a firm basis or for enduring existence.

But you should use the infinitive:

I want to buy a book
I want to found a company

Not

I want to buying a book
I want to founding a company

(Edit:) As KRyan notes in the comment below there is a third possibility:

I want to be founding a company.

There is a slight difference in the meaning between the two. Using want to found implies that this is a thing you want to do at some point, want to be founding implies a particular point in time that you want to be involved in this process (e.g. "What do you see yourself doing in five years?" "I want to be founding a company.)"