Re: besides, in addition to..
Welcome to the forums, Panem.
With questions like yours, it's often best if you write a few sentences in which you're not sure which word/phrase to use.
Regarding the second question, though, I'd say they're all every similar.
Everyone failed the exam except Mary.
Everyone failed the exam but Mary. -- This might read more naturally as "Everyone but Mary failed the exam.
Everyone failed the exam save Mary. -- This usage isn't very common where I am, but it doesn't seem strange to me.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.