TYPO3 Core

I couldn't find any issue about this, so I'm opening one: when installing the Introduction Package with a freshly unzipped archive I stumbled on no less than 3 "not writable" error messages before finally getting to the 1-2-3 screen (and I know from experience that my setup is still not correct, but I'm trying to behave as someone with no knowledge).

I know this is related to the Core, but we should really do something about it.

Furthermore different messages still have different templates, maybe also because some are errors and others are warnings, which is inconsistent (especially the warning (about "typo3temp", since the process is blocked).