Android - How do Google Play app updates work? Are they free?

According to the Google Play Business and Program Policies, you may re-install any app you have purchased, unlimited. (also if the app has been updated since you bought it).

Based on my experience it works like that indeed: I have updated and re-installed paid apps without any issue. Please note that the re-install/update also works on any other android device that uses the same Google account.

When you download an app (whether free or paid), it is tied to your Google account, so you can get all updates for this app as long as the developer is maintaining it.

Every app has a package name. This can be something like

com.touchtype.swiftkey

This is the package name for SwiftKey. If you buy it^*, the app is tied to your Google account. You can download it any time on any number of devices that are linked to your Google account, and as I said above, all updates are free. In case of SwiftKey, we already received two major updates (X and 3). If the guys at Touchtype decided that they wanted more money from us, they couldn't make us pay for updates for this app. There are, however, two options that they could take: make new features available as in-app purchases, or release a new app with a different package name.

^{* You should. It's awesome.}