What is the ruling on purchasing an apartment in installments from an Islamic bank through a Murabahah system, where the bank pays the full price to the seller and contracts with him, then sells it to me in installments with an increase, knowing that the bank imposes a late payment penalty for non-payment, and claims that it does not collect it in cases of hardship, but deposits it into a special zakat fund?

The bank is not permitted to impose a late penalty on Murabaha. If it takes this penalty for itself, it is explicit usury (riba). As for placing it in the Zakat (definition) fund, this is also not permissible, because the defaulter is either a procrastinator, whose case should be referred to the judiciary or from whom collateral and a guarantor should be taken, or he is in hardship, in which case he must be granted a delay, as Allah Almighty says: (And if there is one in hardship, then [let there be] a delay until [a time of] ease. But if you remit [it] as charity, it is better for you, if you only knew.)