You obviously don't have any decompression training (and from what I can tell, you don't even have nitrox training), so don't even bother thinking about questions that involve 100% O2 for emergency bailout use on a recreational dive where you have accidentally gone in to deco.
100% O2 below 20 ft CAN (and probably will) KILL YOU. You also apparently don't understand the concept of SAC rates, as evidenced by your questions regarding # of breaths per minute, which means you have no way of calculating how much gas you need.
Stop and go learn how to calculate your breathing rate. Then stop again and go learn how to calculate how much gas is needed to do an OOA ascent. Then stop a third time and figure out why you are 'accidentally' going into deco with only an Al80 on your back. Now stop a fourth time and think about how you can solve these problems by adding planning and without adding equipment.
Your idea of how you want to use a 13 cft bottle is positively foolish. A 13 cft bottle is completely useless as a pony bottle...really, anything less than 20 ft is silly, as it just doesn't provide enough gas to benefit you in any way beyond extremely shallow depths, except to help you run out of gas twice, rather than just once.
You appear to have come into this conversation already decided that you want a 13cft bottle despite being told by almost everyone that it isn't a good idea. Now, my question is, why do you object to something larger? It's not like a 20cft bottle is that much bigger, and a 30-40 cft bottle slung like a stage would be even better. Of course, even better would be to learn how to manage your gas properly and forget about the whole poco bottle thing, but I'm sure you don't want to hear that.