What would happen under these circumstance

I believe one you probably answered yourself, they can't be written back.

And for number two, that's a good question. After the power failure, if the system can recover to it's previous state, you're probably okay, otherwise, probally same problem.

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I felt so different without a signature.

Answer to your question depends on implementation.
With all apps hosted here, everything is as you said. But it can be done in a different way - via virtual machine or something that could be called a semi-virtual one (doesn't interpret code to be executed but hijacks app's system calls). Such portable app has no impact on a host computer, it just convinces the app that some files / registry entries / ... exist, even if they actually don't. But it's far more complicated w/out proper tools. I know that Thinstall does more or less this thing, unfortunately I don't know any free (even cheap) tool that does this job.