Reloading does not cause an increment.
How about search engines en spambots, are they counted? 70% of the visitors today is from USA, which is very unlikely for a Dutch website.

hi,
there is no option (yet) to ignore bots from counting - so they are counted if they support support ajax / javascript.
Next build will have this option.

Is the counter value reset every night (or is it a total counter) and is the same true for the "Show today" line?
Phrased differently: Should both values be equal and start every night at 0 (if the initial value is set to 0)?

hi,
the counter is updated as required it is not reset.
there are seven sub-counters: today, yesterday, this week, last week, this_month, last_month, and totals which will be updated on request.
you may only (re)set the totals-counter via module settings.   

In that case, I'm just interested to show the sub-counter: today.
Is there an option to skip the counter completely in the frontend?

hi,
you may code you own counter layout.
Copy ."./modules/mod_jsvisit_counter/tmpl/default.php" to directory  "../templates/your-template/html/mod_jsvisit_counter/" (you may have to create this directory)
edit/recode "default.php"
set in module settings the use of "default" layout