Remove a Strip of Hair Color

A: Well, My best suggestion as to ridding yourself of the "strip of color" is to get a hair color that closely matches your natural color and use it to cover the "strip". You don't specify whether this "strip" is the color of the "at-home kit" used or if it is a strip of your natural color, so I am assuming that it is left from the kit.
As to the frizzy patch in the back of your head, I would imagine that is being caused by some environmental factor possibly in combination with the color processes you have had done. Thinning the hair won't solve the issue.
What's needed here is to identify and eliminate the cause of the frizz. If it has always been this way (you didn't specify) you may want to see about getting a straightener to smooth the hair.
If the problem is environmental (being caused by your bed pillow, reclining on furniture, being blown in the car while driving, etc.) you need to be sure to use a shampoo and conditioner to moisturize and smooth the cuticle layer of the hair as well as styling products to control frizz and to eliminate the cause of the frizzing as well. Get a satin pillowcase, or secure the hair when driving, etc.
If properly cared for, you should see some noticeable results and be happier with the way your hair looks.
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See also:
How to color hair
The different types of hair color
How to tame frizzy hair
Why does hair frizz?