Translation:The Swedish Academy has eighteen members.
Normally, the word akademi has the definite form akademin, but since this is a very old organization, they've kept an older spelling of their name, so they still spell it akademien. Both answers are accepted though.
One more thing about this sentence while I'm at it. Normally when we have adjective + definite noun, like svenska and akademin here, we need an article before that. But in names (and similar), like here, we can sometimes skip the article.
Yes. You can be ledamot of things like the parliament or a 'board' of some kind – here you can be either medlem or ledamot, where ledamot is more formal. (we normally use ledamot with the Swedish academy and any parliament, but for boards, both are used more interchangeably).
But for bands and informal groups, you can only be medlem, not ledamot.