I know the Bosmer are renowned for their archery skills, but I was wondering if they are against/for using magic?

They aren't really known for magic, they are rather indifferent about it. They are magical in the sense they have serious connection with the forests of Valenwood and have natural communal abilities with animals. They have "green" magic, but gameplay wise it's not really there (which is a shame).

I would say the Bosmer have a connection to the more physical properties of Nirn because they are also natural alchemists.

I don't see why they'd have a problem with it, though they'd be more inclined to use it for its more practical applications as opposed to anything esoteric. Things like detect life, muffling sound, and restoration would probably be rather popular for most. I'd say alchemy as well, but they can't ingest plant matter, so that tosses a lot of remedies out the window.

There are quite a few in the mages guild. Nothing in their culture condemns it. Keep in mind, they value diversity. They are naturally curious as a people.