Yessss about the separation anxiety from 13 months. No advice as I haven’t figured it out either
Our little boy is at this stage too, he will immediately wake up from being asleep when we put him in his cot. I remember our daughter going through this stage and having to stay In the room and stroke her head until she went to sleep. Unfortunately we have had to leave our little boy to cry it out for five minutes. He does settled after this and will self soothe. Have your tried putting a tshirt u have worn in his cot with him? We found our little boy this really helps.
Can't really help with the second part, but our lo started with the separation anxiety at about 12 months, and he would scream when I left the room even if his dad was there! I found that saying to him "I'll be back in a minute" etc instead of sneaking out of the room really helped, and also if they're at nursery, say goodbye instead of sneaking away. It has gotten much better for us since doing this. Hope it helps you 😊x