Correct, "보다" always means a comparison.

Yes, it's used to make comparisons. You can also write it as ...더 뜨겁습니다 or without the 더

Yes, 보다 means "more than" whatever it is attached to... It is a suffix attached to the end of the object.

Yes, in this case -보다 means than.

If I recall correctly, 보다 is a comparison postfix, so yeah.

보다 is a comparison postfix if I remember well, so yeah.

Yes.

Yes.

I should think so.

Yes

Yes

Not sure if this helps but to my understanding 음식 means 'food' 음식보다 means 'than food'

Temperature