The mass of an object can be subtracted or added. For example, with water, you can just add more to have a larger mass. With ice, you can just chop off a portion to lessen its mass.
Though, if you take a piece of paper and crumple it up, the mass will stay the same.
It just depends on the context of the situation.
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Yes
Because mass is not the same as weight. Weight is mass times gravity so your weight will change if you are on the earth or moon but your mass will stay the same.
Its mass remains the same (except for the very small amounts that stick to the knife blade).
No because now part of the apple is missing so the mass would be less. The total mass of the apple is not changed, but part of the mass is now in the biter's mouth.
Your mass is always the same.