Sakura Solidified Paint Solid Marker, 14 to 392 Degrees F, Blue

Q: Does it work in the rain? Or on wet surfaces?

I think its works in the rain to

Q: Could I use this to touch up white paint on wood furniture? I am hoping to cover a few spots where the dark wood underneath is showing through

Yes, you can. Apply it with a light touch and several coats for best results. The shade of white will likely not perfectly match the furniture due to white having so many possible shades. But, if the area needing a touch-up is small, it'll be good enough. The other answers stating it cannot be used are simply wrong.

Q: Is this marker oil or acrylic based?

I would say that it is oil. It’s waxy like a crayon, it’s not paint. I used it to write on my plastic trash can close to a year ago, and it’s still clearly visible.

Q: Does this work well with tires? Thinking about marking the grooves on my motorcycle tires for better visibility at night.

No not this one. That's why I bought but it scratches off. Use the Hot Max brand of paint markers available on Amazon. They work great. Best ones I've used for tires and for automotive work.