If you want to get off the beaten track in Peru, you need to rent a sturdy 4X4 rather than a car, and preferably one that burns diesel as this is the fuel most widely available in out-of-the-way places. This is doable but costs are generally high. Road conditions are variable in the highlands especially between November and March, the rainy season. Night-time travel is generally risky, not so much due to the potential for violent crime as the risk of running over a pedestrian in the dark, or killing livestock.

Directional signage is marginal on the Panamericana (the main highway connecting Lima with Arequipa, 1,000 km to the south), poor on other highways and non-existent off the beaten track. Locals speak no English so you will be better off if you speak good Spanish (or Quechua, but that's not likely...).

I'm sure you can get from Cuzco to Aguas Calientes (the town below MP) by road. Decent atlases are available in bookshops in Lima (try the "Jockey" mall out on Javier Prado).

I've never driven the routes you mention but my sense of it is that you'd be much better off if you had three weeks or a month to make your destinations by road. You need to be flexible about your itinerary due to the unpredictable nature of road travel in Peru.