What is the ruling on vowing to donate one thousand dinars from a company's funds if the partners refuse to bear responsibility, and is it permissible to pay the amount in installments or by counting invoices owed by the father as part of the vow?

Undertaking a vow is disliked, but whoever vows obedience to Allah must fulfill it. Your vow is a conditional vow, and it must be fulfilled when the condition is met. The fulfillment of the vow is obligatory upon you alone, and you must carry it out from your own money. Your siblings are not obliged to fulfill it. The vow can be fulfilled in installments if you did not intend to fulfill it all at once. If the institution pays off your father's debt, it does not suffice as fulfillment of the vow in place of his debt, and what the institution pays cannot be considered fulfillment of the vow.