I do not think so. There isn't any spot that it could go on these animal shaped humidifiers. Vicks brand has some where you can put the I'll or medicine above the mist area so the water vaor kind of hits it on its way out of the machine. These cranes are hard to clean - I wouldn't try putting anything other than water in the water containment either!
Yes, you should be able to run it for the whole day without running out of water. I run mine at night in my kid's rooms. Be sure to check the mist level to make sure that you don't have it on too high getting everything wet around it!
I am not selling a replacement water tank cap, but you can purchase a Crane demineralization filter instead. Then, if the demineralization feature isn't important, just don't replace it after its lifespan. They sell them locally at Target or also on Amazon.com.