Vinager certanly won't do the job, when you have all this buildup you need alcaline products that opens the hair cuticle for a deep cleansing, and vinager closes the cuticle because of its low pH. So the clarifying shampoo should work. Try using a different brand
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Now talking about lightening your hair, i think it won't damage that much, your hair looks healthy and the shade you want is not that light.
Since you have dyed your hair black i think you should go with bleaching powder and peroxide.
You'll probably end up with either red or orange hair.
If you get red hair you have to use a hair dye with green pigments, something like 7.7 or 8.7 (depends on how lght you wanna go).
If your hair turns out orange then you gotta use a dye with blue pigments, that would be the ash hue. I think a 7.11 would work.
Just be carefull because some dyes like color perfect have their numbers all messed up
Wow, i ended up writing a book here hahahah
I hope that it helps you, i sure wish someone had told me all that when i first started to bleach my hair hahahah