The risk with a locked door is that it might jam in a case of fire so you couldn't get at your dc.
With a gate you can either step over it or haul them over it. I'd say a gate on the bedroom is safer than one on the stairs- less risk of tripping over it in the case of fire.
Basically, you weigh it against the risk of them setting off to explore in the small hours and getting themselves into danger.
Depends on the child. Mine would home straight for my bed, so I didn't see much of a risk there, but some toddlers do go exploring in the small hours and it is hard to have an entire house absolutely toddler proof. Also some parents are heavier sleepers than others: I would wake if a dc got out of bed at the other end of the house, my SIL slept so heavily that her dc were able to cause all sorts of mayhem.
As for the gate on the stairs, you weigh that too against the risk that your individual toddler is likely to fall downstairs. Based on knowledge of toddler, steepness of stairs etc. I had a very unsteady child and very steep stairs just outside the bedroom so that was a no-brainer.
Incidentally, mine never had any problems attracting my attention; often too lazy to get out of bed when they woke- but I heard them all right 
I did have a hook on ds' door when he was a baby for use in daytime because dd would take the advantage of any moment when I was on the loo or whatever to try to break his arms- there were a few months when I really couldn't trust her, so a hook seemed a nice, safe compromise.
We also had reins because I worked out that mine would be spending far too much time in the pushchair otherwise.
But that's all it is: balance, compromise, weighing the circumstances against one another.