Questions about these house's sink faucet's knobs.

The look like Cheng Wong Kong Fung faucets. Have you tried removing the screws in the handles?

They could be anybody's - and they may well be cartridge type that does not have replaceable washers. If they are replaceable washers you will need todissassemble one and take it to a plumbing supply (mabee even some place like Home Despot if they have a "drone" who knows anything) to get the right parts. Washers are generally not manufacturer specific.

You need to remove the bushings around the base of the faucets. Use a good thick cloth and large pliers, the cloth to prevent scratching, to remove t he bushings, after you remove the handles by loosening and removing the scr ews in the center of each handle. Find a handy neighbor to help, this is v ery basic handyman, not rocket science.

The spigot is the exact same shape as my 40 year old Delta.

Which doesn't mean anything as the Ckinese have been cpying popular designs for years.