"- Can I import my existing cracked apps (saved on my Mac) or do I need to re-download through AppAddict Resign app?"
now no, maybe later, for moment you have to download them through AA app, or try resign them by AA Tools if you got backup
"- Will apps downloaded through AppAddict app sync to iTunes or will they error?"
"- Once the app is working, can I use the App Store to update apps or do I need to go through the AppAddict app (and wait for the updated app to be cracked/uploaded)"
you should update them through AA app