I have Zotero 5.0.60 installed from ppa on Ubuntu 18.04.

Disable the annoying window of the auto-update

Answered here.

You have to go in “Preferences” > “Advanced”, then open the config editor (if there’s a warning, ignore, and set app.update.enabled and app.update.auto to false.

Customise the BibTex entry keys format

By default, when exporting to .bib, the label is something like:

foote_probability_1996: all small caps, i.e “author”_“first word of title”_“year”.

I prefer Foote1996.

The setup has to be done in ~/Zotero/translators/BibTex.js file (Your data directory is showed in the advanced preferences).

Make a copy of BibTeX.js to BibTex_AuthorYear.js (or from BibLaTex.js); then edit the following lines:

//%a = first listed creator surname
//%y = year
//%t = first word of title
var citeKeyFormat = "%a_%t_%y";

Now additional changes are needed to make your translator unambiguously recognized by Zotero: at the very beginning of the file, change the dictionary entries for “translator” and “label”. For “translator”, just make sure the new GUID is unique across the existing Zotero translators.

Finally, to keep capitalized author names, modify the citeKeyConversions dictionary to remove the .toLowerCase(). Then, replace the first line of the tidyAccents function:

// replace:
var r = s.toLowerCase();
// by:
var r = s;

And update the fallback list with the capital equivalents.

Also see other bibtex export options in https://github.com/commonman/zotero-bibtex-sb.