Hiya
The diet sodas are a Your Mileage May Vary thing. Some people can drink them, some can't - you just gotta experiment.
It's safe to stay on induction pretty much as long as you like, but personally I found it better to move to OWL after a month or so - I kept the carb levels down at 20-30g but introduced more variety - some nuts and seeds, etc. Just helps prevent boredom

Good luck, and congrats on your start!
Steven