It would depend on the type of frames and headboard. Just mount the headboard to the wall.

Yes, in most cases. Or as above, mount the king headboard to the wall, shove the twins up against. More versatility can be had with two straight side twin upholstered headboards, where either separated or butted allow for twin style sleeping or king with a simple change of bedding to suit either.

If two twin frames with wheels are attached to a king headboard, is there a way to hinge them on the outside so they can swing apart to allow bedsheets, blankets, etc to be put on?

Yes! Attach the single king headboard to the WALL, not the beds. Use a 1 x 4, and get it above any elec. receptacles. Don't attach the holly wood frames at all, especially if on a carpet or area rug! You will find that nothing really moves : ) until you want it to.

If you have two twins together to CREATE the king and plan to use it as a king? You are just making up a KING bed with same size KING bedding,. That means one fitted sheet, and one top sheet. Both king.

Here is the device that allows you to swing the bed frames out away from the headboard.

https://www.amazon.com/Leggett-Platt-Swing-Away-Hinges/dp/B015CCGXRE