There is an analysis of this topic here:
Lui, Dilin. "The Most Frequently Used English Phrasal Verbs in
American and British English: A Multicorpus Examination." TESOL
Quarterly 45.4 (2011): 661-688.
You will need to be a subscriber to TESOL Quarterly or pay for this particular article. However, there is a review of the article on the TESOL blog. Here is an extract from the review:
But, as a teacher who lives in the United States, but has also spent
time in the United Kingdom, I was fascinated by the differences found
in the frequency of some verbs that are common in American English,
but not in British English and vice versa. For instance, Americans use
the following terms much more frequently than the British: grow up,
figure out, show up, check out, pull out, and reach out.
On the other hand, these expressions were more commonly used in
British English: carry on, fill in, hand over, sort out, and pass on.
One of the big differences, of course, is that while Americans fill
out a form, the British fill in a form.
In answer to your last question, phrasal verbs are idioms, and as such are not rule-governed.