Is the white see-through?

Its pretty thick although I have always worn something underneath.

Are the front pockets zippered?

These front pockets are zippered. You can put your phone in the inside pockets. Super convenient for outdoor activities and every casual wear.

Is the material more of a matte finish or shiny?

It’s more of a matte finish, not shiny. It’s fitted so you might want to go up a size if you want a little bigger. I like the long sleeves. Love this jacket.

Does this have any UV sun protection?

I am not sure but the fabric should protect you from the sun.

Can you go running in this jacket in winter?

This jacket is made out of thicker material with all way stretch and thumb holes at the wrist. It would work well for a cool weather run.