I  poured too much oil into the measuring cup, so I poured some back into the bottle.   However, the measuring cup was used for eggs before measuring the oil. I rinsed it from  the eggs but didn't wash it properly with soap, just water. Did I contaminate the whole bottle of oil, or is it safe to use? I put the bottle of oil in the fridge after that and the color and texture changed 
There are lots of potential thickeners, but you often need to select the one that works best with your given need (temperature, if it has dairy, resulting mouthfeel, etc).  In your case, you're already using rice, so you may want to stick with a starch -- corn starch, potato starch, tapioca, etc.  For these, you add a bit to cold liquid, mix it well, add it to the soup and heat it up.  As it approaches boiling, it'll thicken.  You can use flour (wheat, rice, yam, etc.), but in the case of wheat flour and possibly the others, you may have to deal with a raw taste.  You fix this by cooking the flour with butter or oil into a roux, and then adding that, and heating it up to a near boil.  You can also use pureed vegetables.  Cook them in the soup, then put it through a blender so the vegetables add body to the soup. 