Great advice as always from Fullerene.
Question 1: Standing heavy bags are the answer if you have the room to set them up. The only problem in that case is storage, as the bases are large and heavy if you're filling them with sand, which you should definitely do being a heavy weight.
Question 2: This is kind of funny because I sprained my ankle and knee on the same leg in a catch wrestling class last Saturday. I'm a veteran of busted ligaments though, so heres my advice. Take Aleve, as it helps mend ligament damage. Also, eat pineapple like its going out of style, as its a natural healing agent for ligaments. The problem with icing joints is that it can lead to arthritis over time, so I personally don't do it.
Now, you said the joint bothers you when you wake up? If thats the case, you might be doing something to it during sleep. Find a way to immobilize your leg while sleeping to keep yourself from injuring it. I generally sleep with a brace on when a joint is injured, and cut back on blankets, as you can hurt your knees kicking them around if you're a restless sleeper. Otherwise, be very concious of the way you move during the day, as to not put undue pressure on your injured or uninjured limbs, and definitely cut back on sparring. If you're anything like me, or Fullerene apparently, that won't happen, but at least try.