How to add a new word to keyboard by backspacing and clicking on its suggestion? It used to be that if I were to type a new word, like Androidenthusiast, it would suggest other words. I wouldn't select any, press space, backspace, and then it was there as a suggestion. If I clicked on it, it would say "Click again to save", and so I did and so it did. But as of late, it has stopped doing that.

I can't find the settings in Language / input > Keyboards anywhere. Can't remember when its behaviour changed. Nexus 5, running Android 5.1.
The option is gone. It used to be that it just wouldn't show up for those words which were already in your personal dictionary. Now it doesn't appear for any word whatsoever.

It was probably a recent update to the Google Keyboard app which broke this functionality. The Google Keyboard app updates for everyone so it wouldn't matter that my Nexus 5 is running Android 5.0 and yours is on 5.1, everyone got the bad end of the deal.