I don't know of any open source printers, but Brother laser printers are good. Brother is a 116-year-old Japanese industrial manufacturer. Their printers are simple, reliable, they support their printers for a very long time, and they make linux drivers. AND as far as I know they haven't tried any HP-style fuckery.
I also own a Brother printer since I ragequit HP last year. While playing with the settings last week i manually checked the firmware and noticed a possible update. When searching online for the release notes, i found thread after thread of people wanting to revert the update because it blocked third party toners? I hope Brother doesn't go the HP way...
To my knowledge, no—the type of person who would be able to create such a printer usually isn't interested in making printouts. Theoretically, an impact character printer (daisy wheel) is within the range of an enthusiastic hobbyist with enough programming knowledge to write the driver. A laser printer of modest resolution should be within the reach of a skilled team. Inkjet I think requires too many specialized parts.