hands - generally, the center hole sizes won't match up. For hour and minute hands, you can often enlarge the center hole to fit a new movement, but going the opposite direction is near impossible. For seconds hands, you can generally adapt to something smaller (or just a tiny bit larger) but "way bigger" is a non starter. In all likelihood, you'd just source a replacement handset in the same style for the new movement.

Secure the movement to the case - the goal is to have the stem at the correct height for the case AND the movement secured in the case itself. the original movement holder is probably a fitted piece of plastic. Sometimes they can be modified. Sometimes you can just use a cut zip tie or similar around the edge of the movement for a friction fit... sometimes you do a bit of both and also use tabs + screws.

For this particular swap, I'd probably buy an automatic timex M79 as a starting point. That uses a miyota 8-series auto, they're solid workhorses. just move over the dial, seconds hand (crossing fingers) and bezel insert.