1. After each REM period (dreams) we enter an extremely light sleep and sometimes wake up but we then just fall asleep afterwards which is why we don't remember it. It doesn't seem to happen all the time though, only on occasion.

2. As others have said auto suggestion is a good idea, as are alarms though they should be quiet and turn off on their own. You can also train yourself to notice when a dream is ending which can help you wake up/prepare for a DEILD (I did this though I haven't in a while)

3. It's best used while going to sleep or while meditating prior to sleeping. You can do it during the day but the effects won't be as noticeable as if you do it right as you fall asleep. You could also try a WBTB/MILD combination only instead of using a lucid mantra use whatever you want.