I financed my car in spring of 2014, so I can relay what was true at that time, but please take it with a grain of salt since Tesla could easily change their rates/policies in the next couple years.
1) Correct, I had initially planned to make a down payment for 50% of the vehicle's value (financing 50%) but was told that I needed to finance at least 60% to qualify for Tesla's rate. So the maximum down payment allowed would be 40% of the value.
2) The interest per month is not pre-calcluated, so yes, it would technically be possible to save on interest by making lump sum payments. However, there is no easy (ie: online) way to do this. You would need to call Scotiabank each time to arrange for the payment. Doable, but kind of a PitA.
3) My understanding is that making extra payments would only cause your loan to finish sooner. Changing your monthly payments would require a new loan contract.
4) I cannot speak to this whether this would be advisable or not, as my province did/does not offer any incentives.