1 - If dressy casual is the norm, is it perceived as arrogant to dress more formally?
Suggest inquiring as to the reason why dressy casual is the norm - this will be an indicator of how "deviance" (formal dress) is perceived. In my organization, USAID, it is a mark of distinction to have served for many years, beginning with the Peace Corps, and so the norm is a "world traveler" kind of look. If you dress more formally you seem like you don't understand the very specific and unique world of humanitarian assistance. So it's not arrogance that would be perceived, but perhaps lack of subject matter expertise. However, dressing formally is "forgivable" if you are not there as a subject matter expert operationally, but rather an expert of another kind (communications, lawyer, IT, etc.)
2 - Is it OK to dress better than your boss?
Yes. It shows that you are engaged in the job, that you take yourself seriously, etc.
3 - An additional comment
On a branding note, it is important to be consistent about your look and for your look to mean something. My dad has a very formal Eastern European approach to dress, and if he were to change that it would seem odd.
Bottom line - be yourself!