Is it possible to spoil a baby?

Yes. Usually it's the parent that gets spoiled: taking the easy way of giving into a tantrum. When a child learns that a tantrum turns a no into a yes, you've just guaranteed a whole lot more tantrums. In all cases, make the right (not necessarily the easy) decision, and stick to it.
Yes. Well, sort of. Babies get used to whatever they are doing, so at first, if they are always carried, they will get used to being carried, and doing something else is disturbing. Spoiling infers manipulation, and they don't get that right away. By 4-6 mo, they do, and will start to "work the system". So do what you want until about 4-6 mo, then settle into patterns you want to continue for awhile.
Yes. Well, sort of. They get used to whatever you are doing. Spoiling infers manipulation, "if i cry, mom will do xyz for me". So if you carry them everywhere, they will enjoy being carried. Under 4-6 mo, babies don't get the connection, they just know what they are used to and what they like. After 6 mo, they do make the connection, and will start to "work the system.".
Yes. No, i don't believe that's possible. Babies desire some very basic needs: love/protection, food, and to be clean...Not necessarily in that order. That makes them feel safe and happy. So, loving or feeding or cleaning your baby is the right thing to do, and i don't believe doing too much of that will hurt or spoil your little one.