What is "in den Sinn" doing in this sentence?
It is "in den Sinn kommen", a fixed phrase. It's "to cross one's mind", according to this: http://www.dict.cc/?s=in+den+sinn+kommen
in den Sinn¨ is in´t in dative?
No, because of "kommen" which is a verb of motion (even in this figurative sense) it takes the accusative case.
Why not "These and many other questions are crossing my mind"?