Is it Modge Podge that I would use to adhere newspaper to wood?

https://modpodgerocksblog.com/the-7-steps-to-perfect-mod-podging-every-time

Yes Mod Podge works to decopog paper to wood. I think you can add a color to it. What are you making. Good luck,

Modge podge works for that. A layer of it on the surface, adhere newspaper then cover with another layer. If you want let that dry and apply a final coat. I do not see why you couldn’t add drops of food coloring to tint your modge podge. I would experiment on something not important with a piece of the newspaper you don’t care about to see if you like it first and just tint a small portion of the amount of modge podge you need. Don’t ruin the whole jar.

yes.not sure about coloring

Absolutely- have fun!