There are several variables that have to take place for someone to pass fungal candida onto someone else. Most people already have the yeast form in their bodies, and this is common in the oral cavity. So while one person could swap the normal yeast form with another form, the problematic fungal form is another story. Their immune system would have to be deficient in order to for the fungal candida to take hold, and bacteria in the mouth would also have to be diminished. If it did take hold in the mouth, then the ability of the fungal form to spread throughout the body would be affected by other types of immune cells and mechanisms.

Yes, fungal candida can take place without another pathogenic organism being present.

I'm somewhat certain it's contagious through anal sex.