How does it actually work with the installment payments … does the bank want to see the invoices and then transfer the money to you or does it transfer the installment itself?
That's exactly how it works. With general contractors/trade contractors/developers, the bank transfers directly; there aren't that many installment payments. With architects and individual contracts, there are significantly more individual invoices, so the client often receives an advance and pays the craftsmen themselves. They then submit the invoices and receive the next advance. Usually, upon occupancy, you also receive the remainder paid out, for example, to do the outdoor facilities. For the bank, the dangerous phase is then over when the client buys a Lambo instead of building a house ;)
what if the loan amount for house construction is used up but there is still a remaining balance from the developer? Could I then include the grant from the KfW bank at the end or still use equity?? Anyone have experience with that?
You don't have the grant before you move into the house. Therefore, plan an appropriate buffer, either in the loan or as equity. Ideally, both.