It can, but it depends on what you are talking about. You can express "I'm leaving work to go home now" which means your exiting the building of where you work. It does not mean you are quitting your job. "I'm leaving work" can mean you are quitting your job! But as I said, it depends what you are trying to convey!

It depends on the context. Someone could text message you at 6 o'clock asking, "What are you doing?" You could say, "I'm leaving work." That would just mean, the workday is over and it's time to go home. For someone who wants to say they are quitting their job... "I'm leaving the company." "I'm leaving my job."

Not really: "I'm leaving my job" If you have stopped working at a conventional job altogether, you could say... "I'm leaving the work routine" "I'm leaving the working world" "I'm leaving behind the grind"

No, that's not how I'd understand it. 'I'm leaving work' usually means that you're simply leaving your workplace to go home at the end of the day. If you are resigning and not coming back, you'd say 'I'm leaving my job'.