Hit will improve aerobic fitness, if you have the “right” kind of DNA (~20% of people don’t respond, 60% show good results, 20% are super responders). Figures given in fast exercise for a “normal” responder are 10% improvement in VO2 max after a month of doing HIT 3 times a week (insulin sensitivity improvement by 25%).
No need to restrict other forms of aerobic training, from what I’ve read (for example; Peta, who wrote book with Moseley incorporates HIT into a 30 minute cardio workout), but do not overdo HIT training as you can damage muscles & effectivity/benefits decrease.
If you want to determine what kind of genetics you have, only do HIT for a month & compare your VO2 max at end with start. VO2 max is based upon resting & peak heart rates, so compare those (I.e. See if your resting lowers over the month & if your pulse at the end of HIT is higher or stays more or less the same). IAC you’ll likely get an idea by how you handle the training.

I don’t think a month of HIIT 3x a week is going to do a lot for your Vo2max, especially if you’re already reasonably active… will take a lot more than that, lots of factors go into Vo2 max levels.

As for your original question… what are you hoping to achieve exactly? Sure, HIT will improve your cardio, but if you’re planning on running a marathon or something you’ll need to do a lot more than just HIIT to build your cardio (and leg muscles) up to their necessary condition.

Definitely don’t worry about mixing regular cardio with HIIT… most training plans for runners these days (of all distances, sprints up to marathons) for instance all incorporate some HIIT in amongst longer cardio work. It’s pretty standard for most cardio intensive sports these days.

All exercise needs rest days… you have to give your muscles time to repair – the way we get stronger is that exercise makes a heap of micro tears in our muscles, and it’s the repair mechanisms that build it back stronger than before.

That’s not unique to HIIT, it applies to any form of exercise program.

Dr Mosley’s info on HIIT and fasting isn’t really much different to the advice for HIIT by itself… other than, it’s probably easier to execute if you’ve already used up your glycogen stores (simply because it is shorter duration), there is plenty of comments of people in this forum about finding it harder to go for a run the day after fasting (glycogen hasn’t replenished), than it is actually on the fast day (still have some glycogen available)… either way, you’re performance is going to be down a little with fasting, so may as well shorten the time you need to work (at least that’s my understanding of it anyway).

This podcast episode touches on it a bit and was pretty interesting: http://sigmanutrition.com/episode82/

If you’ve never exercised in a long time, then 3×20 s would be a good place to start… but you should listen to your body and try to push yourself a little further each time (assuming you don’t have any underlying heart condition, or other medical issue that might restrict you, in which case please talk to your doctor first).

As your conditioning improves, you will extend things a lot further than that. A popular (and very efficient) form of HIIT is done using the TABATA method (lots of info you can google on that), where you do 20 seconds exercise as hard as you can, followed by 10 seconds rest – and then repeat that 8 times (total duration 4 minutes)… you do that for one exercise. Eventually, you’ll be able to add additional complimentary exercises to your routine (e.g. spin session on a bike, followed by push ups, followed by jump rope).

One other thing I’d add – you should make sure you warm up first… don’t just jump straight into your HIIT workout. If you’re doing it on a bike for instance, maybe ride for 5 mins at a slow pace to begin with and work up to a few higher speed spurts to get your muscles moving first… jumping straight into something high intensity from a cold start could lead to injuries.