I do hope [Harrison's] going to get a legal agreement protecting the amount of money him and ma and pa have put into the property!
He can't. The mortgage providers will insist that they sign a form to say that it is a gift, so that nobody else can claim to have an interest in the property
Harrison and Fallon can grant a second charge with the lender's consent.
They can also enter into a back agreement undertaking to repay the parents if the property is sold. This won't trump the lender's rights to be repaid in full.
In the first case the lender gets first call on sale proceeds to repay the loan. If it is a forced sale by the lender the lender has to pay over any excess after it has been paid in full to the second lender up to amount of the debt.
In the second case the lender won't know but as long as the lender is paid in full it is up to Harrison and Fallon to repay the debt.