1. Most cats are grazers. They will periodically eat a bit and then come back for more later. So just refill that and the water dish when you notice it's getting low.
2. Cats do this to make a surface more comfortable for them. It's like a kneading type of thing. Even though it usually doesn't do anything noticeable, it makes a difference to them.
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"Just drown them in maple syrup. sticky maple syrup." - Taslion