Probably not.
Your best option is install a different camera app from the play store

 

There's a lot of good camera apps to choose from. Most will have many more features than your stock camera app

 

What phone did you have before? I've never met "swipe up or down for zoom" - pinch to zoom is the usual gesture in my experience. And TBH I'd expect tapping the screen to change focus point.

 

Ah, I've never owned a Moto Android, so this is probably a Moto-specific feature.

My alternative camera app (Open Camera) has a "touch to capture" option, though I don't use it: to me the natural use for touch is to select a focus point rather than take an image (though you can set it to require a double tap to take a picture, which does allow you to use a single tap to select focus point). It also has an on-screen zoom slider, but not an "anywhere on the screen" gesture. But you will find that any alternative app will probably lack some of the features of the built-in app too - I mainly use the default app, but like to have an alternative available (it's rare to find any one app that does everything better than another).