some random questions about running with a mask

Don't huff and puff. Run at the fastest pace at which you could hold a conversation or breathe comfortably through your nose. If you're wearing a mask, this will be very slow.

1. There are arguments for and against pausing. If you only care about your actual running pace or distance, pausing could be the way to go because the summary data for a workout and in trend charts will accurately reflect just that. OTOH, you're discarding all the work you did while walking. Your total distance and calories will be lower, as may be your training load.

I prefer to record everything and use manual laps (disabling Auto Lap) to denote meaningful sections. You can set up a simple interval workout that includes a warm-up and then alternates between running and recovery when you press Back/Lap. Garmin Connect will break these out as it would regular laps, and it will provide you with a summary of run time, run distance, and run pace. However, I believe you can only see these on a per workout basis, not in any trend charts. Other software may differ, e.g., if you sync your data somewhere else.

2. Your zones will only be dynamically adjusted if you base them off of max HR, heart rate reserve (HRR), or lactate threshold HR (LTHR), and one of the underlying metrics (resting HR, max HR, or LTHR) is set to Auto Detect and changes. Pausing or not pausing will not change zones. Wearing a mask should not have an effect on your zones, either, since the only thing that should have changed is your pace at a given HR.

3. Maybe. Training Status considers how your Training Load and VO2max are changing with respect to each other. If your zones or max HR are too high, it may think you're going too easy, though technically it should consider your history. However, going from running without a mask to running with a mask has likely demolished your VO2max estimate, because you will either have slowed down drastically to maintain the same HR or have maintained the same pace and seen your HR blow up.

It sounds like you're skeptical of your current HR zones, and you should be. I believe that the watch's default is to derive your max HR from the 220 minus age formula, which is notoriously unsuited to the purpose, and use standard percentages for the zones. Whereas, there are measurable references you could be using instead. Ideally, you would do most of your running below your aerobic threshold, which would define the top of Z2. If you're a more advanced runner, you'll do some speed work near or above your anaerobic threshold (or lactate threshold), which is often the bottom of Z4 or Z5, depending on whose system you prefer. See also this post for tips on setting your max and LTHR.