It was kind of the opposite, AIUI; the Ottomans claimed that Muhammad Ali was just a regional governor, but the country was de facto independent; the Ottomans had no ability to control it.
Oh, no, definitely not. I mean, it was the early 19th century; not _literally having slaves_ was considered a dangerously radical experiment that even revolutionary France could only half-commit to. Freedom wasn't a big thing in the early 19th century.
But Egypt under Muhammad Ali was about as independent as any country was at the time, really. It controlled its own domestic and foreign policy, had its own military, and _invaded its nominal suzerain_, taking Syria off the Ottomans.
Romans also considered Herolds to be a just ruler of an "free" Judea as far as they are conceres. That's how often subjugation works.