This isn't clear to me. The bag (the smaller one that you had before) should fill up fairly quickly when you turn on the O2. Then when you inhale, the bag should empty, or at least mostly empty. Then it should fill up again when you stop inhaling and are exhaling. The flow rate determines how fast the bag fills -- the higher the lpm, the faster the bag fills. That is the only relevant aspect of flow rate -- it doesn't affect how much O2 you take in when you inhale. If the bag does not fill fast enough that it is ready for your next inhalation, you need a higher flow rate. It is called a "reservoir bag," because it holds the O2 until you inhale it. Having a larger bag on there means that you have extra O2 for each inhale, which is fine, but you want to start inhaling as soon as there's enough O2 for you to take a full, deep breath, and not wait for a very large bag to fill. I'm just not really comprehending what you mean by "even at 10 lpm I get enough oxygen for 10 to 15 breaths."
O2 virtually always works. For some people, it is less effective when the pressure in the tank is low (when there is less O2 in the tank). There might be times when it doesn't work, or takes longer to work, but the value of using O2 doesn't really decay over time. Yes, you will use less O2 when you find the breathing strategy that works best for you -- and there is also some evidence that it is just less effective in the first few uses than it becomes after that.