Wood – How to repair leaks in metal wrapped wood gutters

I've noticed a good bit of rain water leaking through what first appeared to be my gutters on my roof. When I got on the ladder and took a few pictures ( attached ), I noticed I've got wooden gutters that have been wrapped with thin metal sheets. The sheets look like they were originally nailed into the wood gutters and sealed around the top / side of the wood gutter. The sealing has started to come apart, and there are missing nails along the length of the metal wrapping.

So my first question is: how should I proceed to fix the leaking? Re-sealing the metal to the wooden gutter and re-nail the metal wrap into the wood gutter ( if so, what kind of sealant / nails )? Replacing the whole gutter system? Replacing the metal wrapping?

The wood actually looks to be in decent shape, but from what I've read, I'd have to paint the gutters every few years, and that's why the previous owners likely chose to cover them ( the whole house is now vinyl sided as opposed to the original wood ).

My 2nd question is: what's a good way to check for damaged external siding (my original concern when I saw there was leaking under the gutters)? Hardly any water is making it into the downspouts that are cut into the end of the original wooden gutter. Instead the water collects at the seam of the metal wrapping and drips down. I can't tell if any water is getting behind the gutters and causing any damage.