Lol, honestly. I’ve experienced that before and when I haven’t slept in a really long time, sure I could feel tired but when meditation is done correctly, feeling tired becomes another passing car while you watch from the sidewalk, just as any thought or emotion
It doesn't usually, however I find that when it does, it's because I am not sitting in an alert position. While it's tempting to meditate on a comfortable armchair, it's not ideal to meditate. I personally find that sitting cross-legged without a backrest makes me alert enough. However if I am meditating on a chair where I can lean back it's far more likely that I drift off if I'm tired.
Yes and no. It doesn't make me sleep but it does "slow" me down which lets me declutter any of the thoughts I've started the day with & get it all in order before charging into the day
Nope. It helps me focus and get into my body and be with myself. (less distracted)