OK let us back up a few steps before the earth falls apart all water disappears so there is no where for us to discover man is truly a land based creature. I have been at this TI stuff for over two years and still struggle with basics. Went to the pool yesterday and just did not feel like things were clicking not matter how much I tried to focus on specific drills. Decision to switch to whole stroke with one focal point per 25, rest and do another. Point being there are times of disappointment but do not let them turn into discouragement. I believe there is a tremendous difference between the two.
To answer a couple of your questions. With all the technology today society is becoming very cautious about privacy issues, especially in locker rooms and pool settings. I would suggest that you approach the director of the pool and explain your situation and the reason for wanting to video tape.
Breathing drill, push off to whole stroke, take no more than one or two normal breaths stop and head back doing some type of balance drill. Repeat again and again . The extra speed and balance from the push off should give you a better bow wave to breath into.
Keep at it.