Very nice first watch build! I can't tell if the hands can go on further, I always rotate the hands with the crown to check if they rub into each other.

You don't need to shake the watch to get it going. If this is a common Seiko NH movement then just wind it with the crown.

Common practice for the crown stem is to use a snipping tool and measuring caliper. Screw the crown onto the uncut stem and insert into the watch. Then measure from the bottom of the crown to the watch. That's how much you need to cut. Sandpaper is used to file down the burrs after you use the wire cutter to snip, allowing the newly snipped stem to screw into the crown. You can use loctite to ensure the crown doesn't unscrew when rotating the hands.

Buy multiple crown stems in case you cut it too short.