Yes, yes & yes. And then yes again.

If you're using cloth or sposies, all poo should go down the loo. And the options to get rid of poo are to scrape it off, use a liner, or to rinse it off. Scraping is gross IMO (I used to scrape) and messy, whereas rinsing it off not only is easier, straight into the loo, but also dilutes the urine in the nappy and saves your nappies. Plus keeps the smell down!
Doesn't water squirt everywhere though? Seen them, but always thought I would end up with poo up the walls