Those are very nice planter boxes, Rebecca. The black lines might just be natural colors of the wood weathering, if they've been out in the rain without any paint or sealant on them. To make them last longer, you could seal the wood with something non-toxic like linseed oil.
Smell the wood to see if you can detect any kind of treatment or sealer on it. If not, I wouldn't worry at all about using them to grow your tomatoes. But I'd only put two plants in each of those boxes - you're trying to give them more root room, don't forget!
What kind of critters do you have around where you live? Daytime pests like squirrels and birds are easy to discourage if you just go out with your hose a few times a day and scare them off. It's the nighttime visitors that plague my tomatoes - raccoons and possums here.
