If I recall correctly, (which, I mean, is sort of a hit or miss proposition) we stopped swaddling at around 4 months. I think the startle reflex disappears by then, and so we just started doing a looser swaddle, then just tucking blankets around her, and then just putting her down with a blanket over her.
That being said, we have started doing a loose swaddle again because she seems to really like it, and for when she falls asleep in our bed and I have to move her, it makes for an easier transition. She also flails her arms a ton when she’s tired, and this helps keep the face-punching down to a minimum.
I think we started putting her down to sleep on her tummy around the same time (4-5 months)
Now, before I get into this, HUGE DISCLAIMER: Everyone recommends you put your baby to sleep on their back. Back-sleeping has been correlated with a decreased risk of SIDS, especially in babies younger than six months. So. Just thought I should mention that for my own peace of mind.
That said, I decided one day, as Olive was having a particularly tough time getting to sleep, to put her down on her tummy. She babbled to herself for five minutes, and was out like a light. I was elated! And horrified! And excited! And conflicted! Because, I mean, wasn’t she doing to die? I checked on her every five minutes for that entire nap, and every five minutes for the next one. I swore I would never let her sleep on her tummy, because then how could I sleep, knowing I was DOING IT WRONG?
Long story short, I continued putting her to sleep on her tummy, and it was one of the only ways she would fall asleep by herself, and eventually she started sleeping on her tummy at night, too. This whole thing stopped working when she started rolling (I think because she wasn’t able to roll before she was sort of immobilized and then thought, eh, what the hell I might as well sleep.) and she has been sleeping on her back again since probably 6 months. She also never really talks herself to sleep anymore, I nurse her to sleep for naps and at night, although I’m sort of working on putting her in her crib drowsy. So far it’s going well, but she’s only 8 months so I’m not too concerned if it takes a while.
I hope that answered your question!