Financing with an additional mortgage on the parents' house

that would be capital procurement on a debt-free property. Purpose-unbound.

Then it needs to be clarified how it should proceed. Does the second property serve as collateral for all liabilities from the entire financing (broad agreement) or only for a certain part (narrow agreement, actually two segmented loans)

But you have to discuss that in detail with the bank, not with us. They will tell you how it should be divided.

Where is that a purpose restriction? One is the collateral, the use is basically irrelevant.

If I have to borrow my 100k on a free and clear house and lose it all in the casino in one day, the bank doesn't necessarily have to care, as long as I can afford the repayment. Alternatively, a big annual vacation in Dubai, new sports car, etc... The bank is allowed to know, but no one will act like a moral crusader (casino) and only possibly appeal to common sense.