Be careful with the term "Intern", because it has a very different meaning in the US. Because you have to be a final year medical student to do rotations in the US, that means we will do them during our internship year (technically our 6th year). We are still considered students during our internship year because we haven't received our diplomas and we haven't even applied to residency yet.
In the US, Interns are first year residents. Meaning they've already graduated medical school and have been accepted into a residency program. If you mention that you're an intern, they will not realize you're talking about the 6th year of medical school and might think that you've already graduated with your diploma and you're now in a residency program. Residents are not qualified for these electives. I know of examples where people encountered problems because for example they mentioned "Alfaisal Intern" in their email signature and the programs in the US thought they were residents, not students.
You want to apply for clinical electives/clerkships, because you need to be a final year med student and those are the ones where you get to play an active role in the team. You'll get access to the electronic records, you'll be allowed to see patients and take history and examine them, and some places will even let you write notes for the patients.
Observerships are something else - you can usually do them whenever you want (not necessarily as a final year student), but you'll only follow the other physicians around and ask questions. You won't be able to see patients yourself, and you won't get access to their electronic records.
Both options are good, but clinical electives/clerkships are better in terms of training and experience.
Most visiting student programs require a criminal background check, and you can use an online one. It should take between 1-2 weeks for you to get the results of the background check (unless you have a criminal record...)