I applied solution from http://wordpress.org/support/topic/no-longer-receiving-alert-emails : "change the main WordPress email to an email on our domain. Before we had the main WordPress email set up as using a gmail account. Once we made the switch all alerts started coming back in. Must be a setting on our new hosting account that differs than our previous hosting".
Now I am receiving admin login alerts from Wordfence.
However, I am still not receiving plugin / theme updates alerts. Right now, Wordfence 5.1.2 is available, but there has not been Wordfence email alert about that.