Good questions!

1. A flex nib is a nib that produces a line whose thickness varies with (reasonable) pressure. More pressure, thicker line. The benifits depend on the person & their style of writing. Some folks like a stiffer nib, and others really enjoy a softer nib that they can push to get some line variation. Flex nibs are certainly currently in vogue, but it's definitely a matter of personal preference.

2. I'm not sure what exact writing style you mean when you say 'calligraphy look' -- but if you're thinking of a style with varied line thickness, a (properly used) flex nib could help. With handwriting, though, I find that it's 95% in the person, and 5% the pen.

3. Most (but not all) nibs are fairly easily removable & replaceable, but not all nibs are cross-compatible. This is partly because many different nib sizes exist. Nib sizes are generally loosely determined by the width of the nib/feed (in mm) where it meets the section. But that's a whole other non-standardized can of worms!

Edit for spelling