Welcome and I'm sorry your kitty isn't feeling well.
First, the number one reason for bathroom habits to change, is a medical problem. Either painful crystals in his urine and/or an infection of his kidney/bladder routes. Peeing in the tub/shower/sink are obvious signs to me, that the cat is telling you, in the only way he knows how...that something is wrong. When it hurts for them to pee in their usual places, they begin looking for other places where maybe peeing there won't hurt; like soft blankets, pillows or clothes. Maybe pee on something smooth and it won't hurt to pee there...they just keep looking for places to 'go' where it won't hurt them.
His vomiting could be an additonal sign that something is not right for him, or he could just be eating too fast. However, with dry food down all the time, there really isn't any reason for him to scarf it down since it is down all the time. This would make me lean more towards him possibly having a bladder problem and the vomitting is a side-effect of those problems.
Best bet is a vet visit to rule out urinary tract problems.