The length of intervals and ratio to rest depends so much on what you're training for and what the desired effect is. For example, if someone says "mile repeats" they may be talking about something like 3 x 1 mile with 0.5 mile recovery at 5K pace, or they might mean a marathon workout like 6-8 x 1 mile at half-marathon pace. Totally different workouts, but nominally both "mile repeats". Physiologically there are differences, and there are so many different types depending on your goals...
However, I think for a few weeks of speed work in a program like yours, the main thing is that you want to be going a hard effort, faster than your race pace that you can repeat for the number of intervals given.
I did some searching and found this to be a decent article but really just covers the basics.http://running.competitor.com/2014/04/t ... ers_8047/5
The speed work in the running room programs tends to be the standard track-type intervals which is described on the last page of the article.
The author says generally you would be doing 2-3 miles of speed at your 5K pace, broken up over several intervals. If you don't know your 5K pace it's not critical, but you want to be doing something faster than your goal half-marathon pace and something you can repeat without slowing down. I think the RR actually suggests 10K pace. The Running Room program has 3 x 1-mile repeats (like described in the article), so I'm not really sure why your instructor is changing that-- but both can be good for a half-marathon program. I assume you'll be doing 8-12 repeats (2-3 miles). One recommendation for speed work is that the hard running shouldn't be more than about 10% of your total weekly mileage.
The article actually says recoveries should be half the time of the interval, but I've normally seen 75%-100% of the time of the interval for short track-type. For your 400m intervals, a full lap at 400m jog will take you more time for your recovery, but she may be doing this to make it more convenient-- it doesn't matter too much though.
eta: here's another good article, and this one does recommend 400m recovery for 400m intervals.https://www.huffingtonpost.com/2014/05/ ... 26926.html