a. It is not yet possible, the tabs reset each time the page is refreshed.
b. Go to the General options -> Sources 2 and select the Producs – Product categories taxonomy: https://i.imgur.com/jBuB1cL.png
c. The keyword suggestions are not same as the autocomplete. The keyword suggestions source is currently not adjustable – it's coming with the next update.
d. Could you please be more descriptive, I don't think I understand what you mean.
e. Same as point b.
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