I have Firefox Focus set as the default browser in the Settings >> Apps menu and that works out OK with most apps, but with Google Assistant it ignores that and always uses Chrome anyway. I just gave up trying to mess with that aspect (... Disabling the Chrome app itself does result in Assistant to use Firefox Focus, but I'm not a frequent Assistant user anyway so as often as I do use it that's not a practical solution. It's just not worth my time to worry about it. YMMV)
But as far as being able to save web sites to the Home screen, yeah it's so simple with Firefox but when using Chrome tap on the three dot icon in the upper right menu bar, tap on More, then Create shortcut.