The 2 induction burners on my current old JennAire cooktop do make
a clicking sound when the burner is on. (And one does need to
have something ON the burner when it is turned on. Mine squeals
when there is nothing on the burner; many just turn off.)
As for the heat, the cooktop retains heat from the vessel that was
on it. I can touch mine at that point. It is not hot enough to
burn me or set anything on fire, but it is hot.
In my other house, I have a new GE induction cooktop. (My love of
induction obviously overcame my extreme dislike of smooth
cooktops.) I looked at every make of induction cooktop that is
around, and also did research online. I saw no real benefit from
the pricier cooktops.