I think three times a week for yoga would be perfect.
And I can assure you that you're burning calories every second that you're exercising.
Yes, short bursts of cardio are as effective as one longer session. And you don't realize it, but what you have planned is really effective for fat burning because your heart rate is going to stay elevated throughout your whole workout. Alternating cardio and strength exercises is a great way to workout!
Good luck on your birthday challenge! It's a great gift that you're giving to yourself.