Thank you very much for the extra info.
There are several things you can do to deter this behavior. She is urine marking her territory. This is common in all cats male/female fixed or not. Females are far less likely to do it, but are more than capable of it.
Try some of these tips to stop the behavior.
You should add a second litter box.
Many times cats do not like to urinate in the same box they defecate in. Nor do cats like to share litter boxes either sometimes. It always a good rule of thumb to follow this formula (n+1= number of litter boxes) N= number of cats in house.
You can use a litter called cat attract. Attract Litter is designed to make it easier to get cats of all ages trained or re-trained to use the litter box. You can get this a pet smart, petco, and larger pet supply stores.
Very important to clean the areas that has been marked. You need to use a enzyme odor eliminating cleaner such as nature's miracle. Regular cleaner such as Lysol will not work as good. He keeps going to the same spots because he smells his scent there. You must get rid of the scent.
I know she has gone down vent, and that is a horrible place for a cat to start going. You can't just pour some cleaner on it. I would take the vent guard and clean it in bleach. Clean the area around the vent with the Nature's Miracle, and even spray some down the vent.
You can also use a product called feliway. This is a pheromone spray that helps cats with aggression, territorial issues, and anxiety. You can spray it on surfaces she has previously urinated on. Pet smart also sells it in a form called comfort zone. This is an electric plug in that puts it in the air.
When you do catch her using the litter box appropriately reward her with a yummy little kitty treat. Cats learn very fast a reward method of training.
If you notice her ever straining to urinate or blood in her urine or stool, then you need to address this as a medical problem and not a behavior problem. Cats will avoid the litter box if they develop conditions like urinary tract infections and such. If this occurs then you need to make her an appointment with the vet.