(Not a teacher)
If you are making statements about the color red in general, you don't need the quotation marks. If you are perhaps selecting among named red shades of paint samples, you might choose the one called "red," and the quotation marks would be used. So number 1 is: I like red.
Number 2 cannot stand by itself as a grammatical sentence because "color" should precede "red;" in addition an article is needed (see number 3). However, you can say, "I like THE red color of her car," meaning either you like the particular shade of red or that in general the red color of her car pleases you.
Number 3 is fine (without the quotation marks).
The comma is not needed in number 4, but if you remove it, it becomes number 3, so I'm not sure I understand your question on rephrasing it.
Student or Learner