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?
Depends if the Portugal authorities changes their mind.
I suggest don’t do it, if possible.
Yes you are correct.