Hi,
I started to learn kanji by frequency usage e.g. by grades (Henshall book), and my first goal is to learn the grade 1-6 the educational kanji ~1000.
I'm at the middle of it and starting to look for a complimentary set of most used by frequency vocabulary?

Did anyone knows a vocabulary list that correspond to each grade, or at least to grade 1-6 as all?

I don't, but you can try bekyo.co/iikanji if you want. They go through the kanji in frequency order, and frequency of reading order. It might help you?

I have an ios app that gives words for each kanji in each grade.... I think. It's called imiwa and it's free. It's a really good app regardless, it's basically a free dictionary.

I was thinking to start core 2k (from smart.fm/anki) but I do not know if they are fitting grade 6 as they include extra sentences as content for the vocab

You don't necessarily need a vocabulary list if you have the kanji list for those grades. For those kanji (taught in grades 1-6) you can simply look up vocab for each kanji with a frequency of >X%.

http://quickkanji.com/

Here you go. Click the link and click "Level" at the toolbar thingy at the top. It will present you with grades 1-6, along with "Jouyou" and "Jouyougai" (not in Jouyou set). Just click the grade you want and it gives you all the kanji of that grade. Hope this helped.