Can Premises Be Singular?

Premises are land and buildings together considered as a property. ... Note that a single house or a single other piece of property is "premises", not a "premise", although the word "premises" is plural in form; e.g. "The equipment is on the customer's premises", never "The equipment is on the customer's premise".

Is it these premises or this premises?

The plural of the word "premise" is "premises." When you see the word "premises," it should be clear from the context whether it means propositions in an argument or property.

Is it correct to say this premises?

Yes, the word “premises” means – a house or building, together with its land and outbuildings, occupied by a business or considered in an official context. so, it makes sense to extrapolate this to an IT term when referring to something being on your property as “on-premises”. It's the correct term to use.