If I am the landlord, and I am collecting monthly payments (in addition to the rent) from the tenants to save them for future (lift, light, gates, etc.) maintenance. Is there a single word/phrase with this meaning for the payment collection?
Property Management Fees are something that you as landlord would pay to a property management company and would include some escrow for maintenance (including emergency maintenance.
Since you are keeping these payments in escrow to pay for routine maintenance, though, I would simply call them Common Area Maintenance Fees although these are normally for commercial properties
A sum of money paid in advance to cover possible future expenses (and presumably returned if unused) is a deposit.
2.1 A returnable sum payable on the hire or rental of something, to cover possible loss or damage.
‘a refundable €100 deposit is payable on arrival at the villa’
A deposit is a financial term that has multiple definitions. The first definition is a transaction involving a transfer of funds to another party for safekeeping. The second definition is a portion of funds that is used as security or collateral for the delivery of a good.