I don't know the exact tech spec, but a very small amount of play will be relatively OK, (a new turbo has none in my experience) If you can noticeably rock it side to side then I'd be tempted to start saving up for when it goes.
The oil will be from the factory breather system. Some oil mist will make it from the sump back through into the inlet system, if there is alot of it, it may be worth taking your intercooler off and cleaning it out with a degreaser.
It may be worth doing a compression check to see how your engines' health is looking.
Any smoke will be an indication of poor engine/turbo health.