Some iPad apps are *TERRIBLE* to use. The interface isn't rendered right, controls overlapping each other.
Others work perfectly.
The Mac App Store is where you download them. I haven't found a way to "browse for iPhone/iPad apps", but if you go to your account, and look at purchased apps, you can select the "iPhone/iPad" tab to see ones you've already purchased. If you search for an app, you can change the results to show iPhone/iPad, too.
But note that not all iOS apps can be downloaded to macOS. Some developers have blocked it. As someone else mentioned, there are apps to download them off your iPad/iPhone and then you just run them on the Mac.