TYPO3 Core

Found the solution :-)

The release notes (http://typo3.org/download/release-notes/typo3-44/) didn't say anything about deleting the files in typo3temp, but the NEWS.txt file in the introduction package did)

So after deleting them and deleting the temp_CACHED_* files in typo3conf the backend appeared normally with compressionLevel set.

There should be no need to clear typo3temp/ because of the compressionLevel.

You said clearing typo3conf/temp_CACHED* is the solution. I doubt that the error was caused by compressionLevel, but more because of the setting $TBE_STYLES['skins']['t3skin'], which is new, but required for all skins in 4.4.
This is in ext_tables.php of EXT:t3skin, temp_CACHED* is a merged file of all ext_tables.php, so this cache has to be cleared.

Clearing typo3conf/temp_CACHED* is also done by clearing All caches or just the Configuration cache (as it is the Configuration cache).

To be honest, I have no idea, whether the Upgrade Wizard triggers a cache clearing. I assume the verisonNumber-Update does, as it writes to localconf.php, which is also cached in the configuration cache.

The gzip compression feature should work directly, when compressionLevel is set and the required RewriteRules are configured IIRC.