The baby eats well. Does it mean they are good at eating with tools?-- No. Unless context indicates otherwise, it means that the baby gets healthy and/or abundant food, or that it eats readily.
The baby eats much / a lot. Does it mean they are good eaters?-- Generally yes, unless the baby is overweight.
I don't feel well. Does it mean maybe I am sick?-- Yes
Just say, 'I'm in a good mood'. Even if you say 'I feel great!', people will still think you are talking about your physical condition unless context suggests otherwise.
A: How are you? B: I am fine. Thank you. How about this "fine", is it about someone's physical condition?-- Unless earlier context suggests that A thinks B is suffering mentally, yes, it is about physical condition.
Can B say as below?-- You can use these:
B: I feel fine. B: I am good. B: I am great. B: so so B: I am ok. B: I am not good