The correct suffix is basically based on who they are, not who you are. Regardless of your current position, you use 先生 when writing to a teacher (e.g., 助教, 講師, 准教授 or 教授). Otherwise, you will use さん or 様 appropriately.
As a professor writing to another professor, should I use 〜さん (like in other workplaces) or 〜先生?
Since you're writing to a teacher, you need to stick to 先生. This is the same even if you are a university president or a Nobel Prize winner. You should not use さん unless you're talking to them as your personal friend.
As a professor writing to a junior staff member (doctoral student or post-doc), what is the right form of address?
- If that staff member holds a title as a teacher, you need to always use 先生.
- If that staff member holds a license such as a medical license, which warrants being called 先生 even by the general public, then you use 先生, too.
- When writing to those who do not hold such titles or licenses, including grad students, post-doc researchers (paid or unpaid) and research assistants, you use さん when they are your subordinates, and 様 when they are outside your research group. In direct conversations, it's generally safe to use さん to address such outside researchers.
I have noticed in some emails that another professor addresses the junior researcher as 〜君, but I am wondering if that is a general thing.
君 is still commonly used in some universities (慶應義塾's convention is well-known), but it's generally considered outdated in business and academic settings. 君 might have been a respectful way of addressing your peers more than half a century ago, but it's now primarily a way of addressing young boys. Some researchers may feel confused or even offended if addressed with 君.