In MineCraft, do free blocks disappear eventually?

No. Blocks don't disappear on their own. Except for leaves, but not player placed leaves.

Yep I think in 10 minutes

Any "Free Floating" items (weapons, unplaced blocks, ect.) will eventually despawn after 5 minutes.

Blocks that have been placed or generated in the world, will remain until certain considers effectively destroy it. Leaf blocks will despawn after some time if it's not within 5 meters of a log block. Snow will vanish if it gets too close to a heat source & wood blocks will "burn up" if they're on fire for certain amount of time (which can spread to other flamable blocks next to it).

With the exception of sand, gravel & liquids… Gravity is NOT APPLIED to blocks, so it's possible to have floating objects.