I've never heard of anyone getting an unsafe package from flathub, but they certainly aren't all as thoroughly vetted as stuff from a well maintained distro. Any major package is almost certainly fine, but if you're downloading something obscure I'd use Flatseal to make sure it's very well sandboxed, just in case.
They've also recently added verified checkmarks to the website for flatpaks that are officially maintained by the developers of the app, so that's another thing to look out for.
Needlessly reductionist, but also wrong. If your code is proven to work (like, machine verified), and you use a compiler that is also verified to generate correct code, then that code is secure.
Flathub apps will likely be removed quickly if they're found to be malicious. They're slightly more unsafe than official repos, but you should be fine. Make sure to carefully check apps with like 4 downloads though.
Even disregarding the trust issues with Flatpak packages made by random people: Packages often contain versions of some libraries in order to not depend on the distro's. If there are security vulnerabilities in a library then the distro maintainers usually fix it very quickly (if not go find a better distro) and it's fixed for all packages on your system that depend on it. But this doesn't apply to Flatpak where the package providers have to update the libraries in their own package - and the track record isn't great. Sandboxing doesn't help if that vulnerability leads to wiping your home directory.
They aren't inherently safe. I don't have any examples of Flatpak packages off FlatHub being poisoned, but FlatHub does allow "community" maintained packages - as in, someone unaffiliated with the development team of an app packages and publishes the app to FlatHub. That would seem to be a really good place to get into a supply chain if you were a bar actor.
Flathub is likely safer than most other places to get flatpaks from, certainly safer than just some random repo you find on some guy's website somewhere, but no software source is guaranteed to be 100% safe.
Therefore, the answer is that Flathub is not always safe to use. However, I do not know of any package source that is always safe to use. Is Flathub more insecure than other package sources? I can't answer that because I don't use solutions like Flatpak, AppImage etc. myself.
It's more about trust, than security. When you use a specific distro, you only have to trust the distro packagers. These packages are reviewed by multiple persons, tested thoroughly and (usually) built in a reproductible way. The packagers are usually different from the developers, so they can also review the code itself and eventually patch issues if needed to be in line with the distro's ideology.
With flatpak, snap and friends, anyone is a potential packager, so for each software you gotta trust this single entity, which is usually the developer itself.
The general community is probably going to catch any issues that pop up extremely quickly. Like my main machines are all on whitelist firewalls residing on external devices. If any software tries to make odd connections, the connections will get dropped and logged. I wouldn't hesitate to report anything odd. I don't run sketchy proprietary junk for the most part.
I think so. In some cases the flatpaks are prepared by the developers themselves. This isn't in itself a sign of trustworthiness, but if a dev were to sneak malicious code in somewhere and it were found out... Well, the internet is the courtroom, and the public the jury, right?
But, it is a piece of software, and you never know what one little dependency can do. Same can be said about repos.