Indeed. Once a situation is suspected to be done by criminal intent, investigators can interview personal, go through search histories, looking for text conversations and so on. Once collected a judge can look at it and determine if there is or isn't intent.
It is a costly, time consuming and cumbersome process, but the legal system is quite used to it since almost every single criminal case involve some aspects of establishing intent.
Yes but it is much more dangerous to assume that correlation can't imply intent. Because sometimes it does.