Anytime I picked up my kids when they were crying in bed it was nearly impossible to put them back down. Seeing me makes everything worse Last night my 13 month old was crying so hard after I put her to bed and I couldn't handle it either so I went in and rocked her. She cried even harder when I left the room but then fell asleep right away.
Just know that naps suck at this age. Babies put up more of a fight, the naps aren't very long and parents tend to get super frustrated by this.
For night time sleep, I would recommend doing your normal bedtime routine, put her in her bed, awake or asleep and leave the room. Give her 15 minutes and if she's still crying, go in and rub her back then walk out again. Give her another 15 minutes and repeat. I've never had to let my kids cry/fuss longer than about 20-30 minutes. I've given this advice to a ton of people and they all say it works like a charm. You just have to be consistent no matter what you do.
Answers
This is a tough one. 5:30 seems a little early to me but when is her last nap?
I have never been one to follow the whole "drowsy but awake" thing with either of my kids so I'm no help there. I don't think that rocking a baby until they are asleep then putting them in bed will do any harm or create a bad habit. I did it with both of my kids until they got older and stopped falling asleep drinking a bottle.
This could just be a random phase that will pass. IMO sleeping is really tough and all over the place until about 9 months old.