The smallest known insects are parasitic wasps in the families Mymaridae and Trichogrammatidae, both of which contain some species that are less than 0.2 mm long as adults. This is actually smaller than many single-celled organisms; here's a picture of one to scale with Parameceium and Amoeba (from Polilov 2012). Despite this, they still have fully functional eyes (or at least females do, males are often eyeless). Though their visual acuity can't be very good since they only have a few dozen ommatidia, each of which is something like 5000-6000 nm across, which is barely much bigger than the range of wavelengths of visible light. If you're willing to count simpler eyespots without any real image resolution capabilities there may be smaller contenders though, like tardigrades as previously mentioned, or maybe some flatworms.

As for your second question, there are many single-celled eukaryotes which can at least detect light in some way, though probably the most impressive eyes among these are found in certain dinoflagellates. Some species have structures called ocelloids, which are complex camera-type eyes composed of multiple organelles, including a cornea made of mitochondria and a retina formed from modified chloroplasts (Gavelis et al. 2015). Even some bacteria can be surprisingly good at detecting light though, with recent work showing that some cyanobacteria can effectively use their entire cell membrane as a spherical lens to track light sources (Schuergers et al. 2016).