Not exactly either. Tesla says that they'll roll out in US first (west coast to east), then EU & the rest of the world; priority will be given to more expensive configurations first and existing customers will only get priority within given price tier.
Therefore, the fastest way to buy a Model S is to live in the US, immigrating as necessary, buy a Model S and order the most expensive Model 3 you can configure ;)
Yes, but you will still need to make the $1000 deposit...
if you have a Model S or Model X $1000 is probably nothing
Existing customers will get priority. I have to say, I did lol when reading that but it makes sense to give a little goodie to your existing customers.