Try rechecking your toilet connectivity and then see if there is a something that hinders the water flow to your tank. If needed you must replace bobble so that no excess water will flow to your bowl...
Try checking your toilets valve if it needs to be replaced and also check if there is there is something wrong with the way its connected to your toilet...
In my opinion, two drains is best as long as the are not joined on one pipe because in that way the water and waste that are filtered on it won't get stuck...