Yes I want <to>.

[asdasdasd]

1. Do you want some coffee?

Yes, I want.


1.1. Do you want to drink some coffee?

Yes, I want to.


So is it true that when we ask about an object we don't use to (1) and when we refer to an action (2) we need to [and it's like the rest of the phrase (drink coffee is elided?)]. Is it a good rule that explains this phenomenon?

 

[owlman5]

1. Do you want some coffee?

Yes, I want.

This answer to the question is strange. These answers are normal: (1) Yes. (2) Yes, I do. (3) Yes, I want some.

1.1. Do you want to drink some coffee?

Yes, I want to.

This answer is reasonable. You can also use Yes or Yes, I do.

 

[suzi br]

1. Do you want some coffee?

Yes, I want.


1.1. Do you want to drink some coffee?

Yes, I want to.


So is it true that when we ask about an object we don't use to (1) and when we refer to an action (2) we need to [and it's like the rest of the phrase (drink coffee is elided?)]. Is it a good rule that explains this phenomenon?

Neither of these sound right.
Much more likely answers to the first one:
1.Yes, thanks.
2. Yes I do.

It’s unlikely to even ask the second question.

 

[entangledbank]

These short answers have to end in a modal/auxiliary verb, or 'to', not an ordinary verb. Despite its meaning, 'want' is an ordinary verb, unlike 'can' or 'will' etc.:

Yes, I can.
Yes, I will.
Yes, I want.

So to answer a 'want' question in this short way, you have to either change it an auxiliary or add something:

Yes, I do.
Yes, I want to. [if 'to' is appropriate in the longer form: I want to drink]
Yes, I want some. [if 'some' is appropriate: I want some coffee]