Can the filtering equipment (pumps, filters, heater) be installed outdoors?

Yes! All the main pool equipment manufacturers design their equipment for outdoor installation. There is no need for a “pool house” or “shed” in which to store the equipment. Try not to allow the bushes to overgrow the equipment (especially heaters) which will allow for moisture buildup and keep the mulch away from the vents on pumps and heaters. But overall, the equipment will operate maintenance free for years even if left out in the elements.