You have 10 posts, so you can now upload pictures. Please do so, it's helpful and we like to look at them
For your brake, it could be a couple things.
1. Your cable is too short and needs to be let out a little.
2. Your cable has excessive friction and as a result the calipers do not fully release because the cable becomes stuck before relaxing to its zero tension position. Solved with any number of the following: new cables, new housing, making sure the cable has gentle bends from the lever to the caliper, taking the caliper apart and cleaning it.
As for your wheel, it could also be a few things as I'm not entirely sure what you mean by having some 'play'. Is the rim wobbly, or does the whole wheel knock about laterally when in the frame?
1. The spokes have relaxed over time and need to be tightened or loosened to 'true' the wheel. Check for this by sighting parallel to the rim's braking surface and spinning the wheel.
2. The rim itself is bent. No big deal, the quick solution is to true the wheel just like problem
#1 . However, it almost certainly won't be able to become 100% perfectly true. To do that, you'd have to take apart the wheel and bend the rim, and then rebuild the wheel. I don't think that it's worth doing that for this bike unless the wheel is
severely wobbly and is incapable of being trued.
3. The hub is loose, and needs to be tightened. You can check for this by rocking the wheel laterally while it's attached to the frame. If there's knocking, you need to get some cone wrenches and tighten up the hub until there is the barest hint of play when the wheel is off the frame, and disappears once installed on the bike.