Currently hold an F1 visa (not sure is valid), but will travel for an academic conference, do I need to apply for another B1?

I am not sure if I can enter the US with my previous visa or do I need to apply for a B1 instead.

Yes, you have to request an new B1 visa.

Typically your F1 goes accompanied by your I-20 (document provided by your university) that you need to show at the border. Even though your visa was not invalidated, your I-20 for sure is. Unfortunately, I don't think you hold any chance to make it through the border, and if you do, it will be a risk situation for you.

More info here: Status and Nonimmigrant Visa Violations

And if I do apply for a B1, can I be exempt from the interview and just mail my passport to the consulate

I am afraid that the requirement of an interview will not be waived due to the fact that you had a previous visa.

The Drop-off service apparently seem to require that you apply for the same kind of visa;

"You must be applying for the exact same type of visa. For example, you had a B visa and wish to apply for another B visa"

as you can read more carefully here: Applying for a Visa without an Interview (in the case that your country is China), although I believe similar policies will be applied for neighbouring countries.