The problem set you are looking at is attachment based and stems from being abused or neglected in her early days, which resulted in her gaining to feel secure or proper connected to her primary caregiver.
Pleading for stuff is seeking connection and reassurance that you are there to give her what she needs and to love her. She doesn't understand this yet The tantrums are bewilderment. Please be very gentle with her and try not to shout even though you are feeling frustrated. Reassure her that feeling you really, really want something is fine, but ask her to trust you when you say Not today, or Later. Each no should be accompanied by a hug.
Ask her to understand that when you tell her No you have a loving reason for doing so, that you are her mother and you will only give her what is good for her. You can ask her not to keep on asking when you have said no, but compliance here will take time to develop.
Make sure you follow every No with a hug and 'I love you'. Try distraction too, especially if it involves doing something together.
Hugging strangers is a sign of complete lack of attachment to a single, loving caregiver and/ or negligence-abuse in early years. You can try talking to her about reserving put hugs for the people we know who love us, and list those people.
The stripping off isn't necessarily autism - some children find it very hot when they come indoors compared to the outdoors.
It may also be in the same category of behaviour as the hugging strangers - a poor sense of boundaries due to abuse or neglect and attachment absence as a baby and toddler. I would teach her that she can dress in indoor clothes inside the home, and that the people who love her would like to see her dressed. Tell her that mamas and dadas always dress their babies. You can help her to dress even though she's a bit old for that. A lot of your work here will involve 'reparenting' and treating her as if she's a few years younger than she is
Playing with boxes or polystyrene isn't an issue as long as it's imaginative play. Breaking toys is telling you she doesn't feel worthy of nice things, or a pre emptive destruction if she has had the experience of her things being broken, taken away, or given to others. If she breaks things by accident, it may be that the things she has are not suitable to her style of engagement with them or geared to someone with different interests.
Calling you mama and dada and wanting to be held like a baby is a sure sign that she needs you to parent her almost as if she were starting her life all over. She feels like a baby.
This is good. She is allowing herself to be vulnerable with you. I would do all the holding she can take if I were you. The eating thing is the same. Maybe let her sit on your lap while eating. She wants the security of being babied.
I would be very curious if I were you about the reason she was in foster care, and her experiences while being fostered.