i/ That's because of the cache of joomla. Please make sure that the cache option in the configuration of joomla and the system cache plugin are both deactivated and you should not have that problem anymore.
ii/ Your settings means that your users cannot checkout without registering/logging in. That doesn't mean that they can't add products to the cart.
If you won't want that, you will have to configure access levels to your products prices so that your users don't see the product price/add to cart button when not logged in.
iii/ That's not possible. Each guest has its own cart.
Note that if you're testing with the same browser, the session is the same, so you're the same guest...
Now it might just be a display issue because of problem i/