Toyota Aurion 2008 Problems

I'm afraid the Corolla and Aurion are actually two separate models, but you'll find price and spec details on the 2008 Aurion here, and the 2008 Corolla here.

If you want a workshop manual I would suggest you google Toyota workshop manuals, or go to ebay.

Convex mirrors are not unsafe, they just need the driver to take a different view.

If it is only a slight leak you could probably continue to drive it, but if you did it would only get worse and you will eventually have to replace the pump at your cost. I would accept the offer.

It does seen unreasonable to have to remove the engine to fix an oil leak at the timing cover, I would take it somewhere else and get another quote. Oil leaks are not uncommon on Toyotas, as they are on other models, so I would doubt that you would win an argument that it wasn't wear-and tear. If the leak isn't a bad one then I would think you could carry on for some time before you needed to have it fixed.
 

I would swap tyres from side to side, as tyres can often be a contributor to this sort of problem.

You say the car had a poor service history when you bought it, and there was sludge under the filler cap. Both should have been warning to you that this car hasn't been well cared for; you are now paying the price. Sludge builds up in the oil galleries when the oil isn't regularly changed, and if let go long enough can cause blockages that can be fatal to an engine. It's rattling, using a lot of oil, and blowing a lot of black smoke, you should have it pulled down and inspected, and possibly rebuilt.
 

It's good to hear that your car was fixed; it's also good to hear that there are still mechanics working at dealers who know how to fix cars and not just replace parts.