Would this lens fit on my Nikon D5000?

Would a NIKKOR 50mm AF f/1.8D lens fit on a Nikon d5000?

Yes, but it won't autofocus, you need the AF-S/G version for that.

Yes. Just focus manually and it will take great pictures. I have older Nikon lens for my new Nikon that works great on manual focus.

It will be fine if you don't mind manually focusing it. Only Nikon AF-S lenses will auto focus on your D5000.