This projector worked well last time it was used. There's no remote. Controls are on the top of the unit.
Here are the specifications - https://www.projectorcentral.com/pdf/projector_spec_3551.pdf
"The Sharp XR-10XL Multimedia Projector is perfect for use by mobile professionals and educators. It offers brilliant, high resolution images and quality that you can effortlessly control. 2000 ANSI lumens illuminate your video, photos, and graphics while the 2000:1 contrast ratio ensures clarity and sharpness. The 4-segment color wheel, in combination with TrueVision, delivers superb color, brightness, and reliability. A wide array of input options lets you select the source you want, for flexibility in your presentations. And at only 8.6 lbs, it travels with you easily, fitting into a travel bag or carrying case. The whisper quiet operation and long lamp life (2000-3000) subtly improve the viewing experience for you and your audience while the wireless remote lets you command your presentation from anywhere in the room. A good projector can help you look prepared and professional in addition to boosting your creativity in dispensing information. Order yours, get presenting, and let the Sharp XR-10XL make you look good."
Remotes are available on ebay e.g. https://www.ebay.com/itm/222759431144
New systems are available from authorized dealers for $749 - https://officewonderland.com/listings/sharp-xr-10xl-projector/