You are allowed to pick him up, that's no problem. Free roaming is really only suited once your bunny is litter trained. When they have more space, it can be harder for them to learn to litter train. So it's better to start with them just in their cage, or with a small playpen around around it, and once his litter habits improved, then you can increase the size of the area he has access to. If he continues to have good habits you can increase the area more until he's free-ranging again. If he starts having bad litter habits, you can decrease the size of the area again to help him get it right.
Keep in mind that a litter-trained rabbit should do all pees in the litter box, but will probably only do 90% of poops in it. Few rabbits have perfect pooping habits, and when they are new to a home, they will often poop around the place more because it's a way they use to mark their territory. This could be one reason he still poops everywhere. For your litter box, you can have newspaper in the bottom, but it's good to have a layer of litter to absorb the pee, either newspaper pellets, wood pellets, or carefresh type bedding. Wood chip bedding may not be suitable depending on what kind of wood it is, and depending on your bunny he may be reluctant to use it if it's too hard on his feet. Do you also have hay in or over your litter box? Rabbits like to poop and eat hay at the same time. So putting hay at one end of your litter box is a good way to encourage it's use as well. Make sure you don't have bedding elsewhere in the cage, as that may confuse your rabbit as to where to go.
