Hi Rainbows,
In a past life I used to repair power tools, so the way I would approach this would be:-
Do NOT remove the armature bearing yet. Reassemble the drill, not worrying about the motor brushes. No need to remove the gearbox grease, or if you have already removed it, no need to relubricate it just yet. The main criteria is that it all turns.
Make up a rod, about 6-8" long, from steel bar or rod that you can grind the end down to be a snug fit in the hole for the chuck key in the chuck. Hold the drill in one hand, with the rod stuck in the chuck key hole, and give the rod a good whack with a big hammer. This should loosen the chuck which can then be unscrewed by hand. Sometimes several whacks are needed, but this is the best way to loosen screwed-on chucks. As John Reese has said, the inertia of the armature and gearbox will be sufficient to resist the rotation.
Then dismantle the drill again. As you thought, if you try to lever the bearing off, you WILL damage the commutator. What you need is the bearing separator shown by John Reese, but these are rather expensive for a one-off. You could probably bodge something up. The advantage here is that as the bearing starts to move, you can tighten the separator jaws under it, so getting better purchase on the bearing. If you cannot sort out something here, try to see if a garage or auto-electrician can remove it for you.
When you have dismantled the gearbox and removed the chuck, you should be able to see how to remove the gear and chuck bearings. Then wash out the gearbox housing (kerosene or similar), replacing any bearings that you can, reassemble and lubricate it. I like to use a grease with Molybdenum Disulfide in it as you are unlikely to take this apart to lubricate it again.
The best way to clean out the windings of all the accumulated crud in there is just to give it a really good blow out with compressed air. I would prefer not to poke at anything, just to give it a prolonged blow-out. Poking could compromise insulation that old, and anything left after a really good blow-out would probably not affect things too much.
Hope that helps and have fun with your new toy.
Cheers, Stephen S.
Edited By StephenS on 24/05/2016 04:02:30 (Edited for spelling)
Edited By StephenS on 24/05/2016 04:03:21