How is movement of proteins and lipids between different domains of cell membrane prevented?
Why is the noncytosolic layer not able to do lateral movements between domains but cytosolic layer is able to do so?
There are various mechanisms through which membrane proteins can remain localized in the membrane. See the below figure from MBOTC (book):
(A) They can aggregate together so that their relative positions are constant.
Where did you read this. Both layers can do lateral movements; if proteins are specifically "anchored" to one side of the membrane then the concept of domain applies to that side only.