The Arch repos only host the latest version of a package, so usually you can't install older versions of a software. There are some exceptions (like with PHP or Python, where you may require a specific version of the framework), but there's not that many of them. You'll see that it's usually not a problem, as it's still recommended to run the latest version of every software, for the security patches.

If you update your system constantly, there shouldn't be any compatibility issues with the updates. The official repos are carefully managed so that, at any given point, every package works with every other package. If a common library is updated, all the packages that depend on it are recompiled and updated to use the newer version.

If you stop updating your system, everything that you already have installed will keep working as it was.

For a while, installing new apps without updating will work flawlessly. But after a while, the new apps will start becoming incompatible with your system, due to outdated libraries and missing dependencies. In that case, you'll need to update the system so that everything is up to date again and it works. The package manager will prevent you from messing things up, so don't worry that much about it.

Arch is a rolling release, so it's designed to be constantly updated. That's the way I recommend people use it, especially if they're new to the distro. But if you don't inatall new software, it's also perfectly stable without updating (and you can also install new software without necessarily updating everything, if you know what you're doing).