I wouldn't bother with removing the old insulation. If you haven't caught histoplasmosis yet, you probably won't. Just lay new on top of it and go on. If you're at all concerned, bear in mind that the greater risk lies in removing the old insulation. If all you're doing is adding on top of it, the amount of disturbing you're going to do to the bird poo is marginal - you're just going to lay more insulation on top of it. Put on a dust mask and you'll be fine.
Read up on what causes ice dams. Your roof is warm, which causes the snow to melt and melt water runs down the roof, under the snow...until it gets to the cold eaves (cold because they don't have a nice, warm house under them), where it freezes again. Ice builds up, water pools behind the dam and creeps under the shingles, until you've got water leaking inside.
Several solutions will help:
1) Ensure good ventilation in your attic.
2) Absolutely upgrade the insulation above your ceilings. The less heat there is coming up from below, the less heat there is to melt snow.
3) Strongly consider providing ventilated insulation on the underside of your roof.
4) Eave melter strips. This is expensive but can be extremely effective. It's just a low-temperature resistance heater that melts the snow at your eaves. It doesn't have to be kept on constantly, just cycled on and off a few times per snow to keep the eaves clear.