What is the ruling on purchasing household furniture in installments due to inability to buy it in cash, and what is the ruling on collecting employees' installments and remitting them to the installment company in exchange for obtaining a percentage of the remittance?

If purchasing items for employees by installments is Islamically permissible, then there is no objection to you collecting the installments from them and submitting them to the installment company. If you wish to receive a commission from the company for this work, there is no objection to it, as it is a type of brokerage. However, if you wish to receive a percentage from the employees, you must agree with them on a known fee or a percentage, and this work is considered an agency for a fee.