From 1 April 2018, Stooq Metastock/Ascii databases will not be available anymore

We don't use those databases.

Amiquote will download data after 1.04?

I am not fortune-teller so I can't tell you what will happen in the future. I am just saying that AmiQuote does NOT use the link you have listed.

So, Amiquote will work with stooq in spite of they are going to stop update Metastock/Ascii databases?

I already wrote, we do NOT use Stooq databases from that link. And as I wrote, I am not fortune teller and I can't tell you whenever the world will continue to operate tomorrow the way it operated yesterday. Third party web pages operate on "as-is" basis. They can change everything everyday as they wish.