"Cooker" is not a word. You can say "good cook". You cannot say "good in cooking". You could also use the word "talent" which is a word used to describe something we are good at. I am good at cooking. I am a good cook. Cooking is a talent of mine. I am talented at cooking. EDIT: "Cooker" is not a word used to describe a person, it is an appliance.

US: A "good cooker" is a pot or appliance that heats up food well. You are "a good cook" or "good at cooking."

Something to be aware of ... 'I'm a good cooker' may not be correct, but it is still very commonly used in informal conversation in my part of the English speaking world. I'd advise sticking to 'I'm a good cook' and only use the imformal or slang form if you hear other locals using it and you want to adopt their manner of speaking.

No. You need a determiner, ‘cause people would not know that are you a person, or 2 people.

You can say "I'm a good cook." Correct, "good in cooking" is not idiomatic.