This might be a silly question but, I rather get a concrete answer.
Do you still qualify for the golden visa if you buy a property for €500,000 with a mortgage? That is, you put a €50,000 down payment and mortgage the rest; or do you have to invest the entire €500,000 up front?
Thanks in advance! 
no, the whole point is that they want 500k to cross the border into the country. I recall you could mortgage amounts > 500k, e.g. you buy a 1mm house and finance 500k of it.
I have heard that as long as you get the loan OUTSIDE of Portugal, you can use a loan to fund a property. (i.e. obtaining a HELOC on a property you own in the US and paying all 500,000 for the GV investment using a combo of cash and HELOC funding…then you just pay down your HELOC as you would a mortgage)
You can only mortgage the amount over the 500,000 investment if you get the loan INSIDE Portugal (i.e. paying 500,000 down and getting another 250,000 loan to buy a property valued at 750,000).
Can anyone verify if this is accurate?
I would also like to know the answer to getting a loan outside of portugal. My aim is to open a company in another EU country, and use that company for a loan from that country to finance the purchase in Portugal. Any lawyers know the answer to this question?
Yes you are correct.
What the authorities (SEF) need to see is the full investment amount (e.g 350k/500k) come from outside of Portugal into a Portuguese bank account.
If you wanted to buy a 600k property then you could invest 500k cash and take a 100k mortgage in Portugal. You’d still qualify for the GV under such circumstances.
Alternatively, if you were to take a loan or remortgage a property in another country to finance the entire investment (e.g. 350k/500k) then that’s technically also possible.