Since she was 4 weeks early you can expect her to hold her head up properly in another month I guess. Did you consult a paediatrician?

Probably at 8 weeks babies heart beat can hear through early ultra sound... sometimes at 12 weeks too,so it depends on individual,your Gynaecologist will tell you everything...
Don't worry,
Consult with your Gynaecologist and clear all your doubts...

Has anyone behaved like this in front of your girl?
Talk to her normally about it and be strict and say no whenever she repeats it in front of you, take help from people around her at home and school so that she learns it is wrong and talk to her understand why she does it. If she isn't understanding then you can also consult a child psychologist, they can help.

Bullying is not good behavior and can really hamper your child's emotional sense

I wont call it as disorder...I m not sure who calls this as disorder....hyperactive is a positive term...just need to curb it down may be talking to the baby...understanding babies needs etc. Try to guage where ur child's interest are..try to let him spend as much time in it...don't worry this shall pass soon.

Since he is 11 yr old boy he can easily explain his reason for anger.. Did you ask him what's the reason?
Do you have another child? As in your profile it is showing you have a 1 year old boy...

It will eventually go...try to distract her when she asks for...

You can go to daycare and stay for some time. The underlying cause for this is separation anxiety. This is when children are unable to separate from their primary caregiver, which in your case is you. In such a case, taking some time away from your child is crucial. This means at home making sure your child interacts with other members of the family. This includes your husband and any other children there. Also taking your child to play in the locality will also improve this. Every day you should spend at least 2 - 3 hours away from your child and ensure. This will increase your child's independence and reduce your child's reliance on you.

It's common thing for kids,it will take some time for them to adjust in school,you too encourage him for going school...

You can Google

Consult a psychiatrist for this matter