True, perhaps finite is a better word.

During development yes, but not as adults. All flying insects have determinate growth, meaning that they go through a specific number of stages before reaching a final adult stage, at which point they no longer grow. This is in contrast to some other arthropods (e.g. spiders, lobsters, and some non-flying insects like silverfish), which can continuously molt and never really stop growing. In all flying insects, only the final adult form is capable of flight (with the exception of mayflies, where the last pre-adult stage can also fly), so any time you see a flying insect, it's already in the ultimate stage of its life and won't grow any more.

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).

Generally yes, and the other answers already do a good job of explaining this, but I want to point out that there are real-world cases of genes which do not follow this model (and not just due to post-zygotic lethality of some genotypes as already mentioned). This is called segregation distortion or meiotic drive, and involves one allele (or often a group of linked alleles) increasing its own chance of being passed on at the expense of alternate alleles. Mechanistically, there are various ways this can work, including such a gene ensuring that it ends up in an egg cell rather than a polar body during oogenesis, or in some cases actively killing any gametes which don't share the same allele.

Besides these cases where meiotic drive is inherent to part of an organisms' genome, similar inheritance patterns can also be manipulated by parasites or pathogens. Wolbachia bacteria infect insects and are passed on from mother to offspring via eggs, and have famously developed ways to manipulate their hosts to produce only female offspring so that they don't end up in a male (which would effectively be a dead end). Humans have also been experimenting with the use of meiotic drives for artificial selection purposes, including some recent high-profile studies into the use of such a mechanism to reduce the ability of mosquitoes to transmit malaria.

These terms are inherently relative rather than describing any definitive thresholds, but among insects hunting wasps and solitary bees are perhaps the most "K-selected". These species provide significant parental care to offspring in the form of food provisions (pollen/nectar in bees, and usually other paralyzed arthropods in wasps) and as a result have relatively low reproductive output on a per-individual basis.

For example, Punzo 1994 studied the tarantula hawk Pepsis thisbe, for which he estimated an average lifetime fecundity of 13.4 eggs/female. As you can imagine, the process of hunting down and paralyzing a tarantula, digging a nest, laying an egg, and burying it takes many hours. Also in line with the general traits of "K-selected" species, these offspring have fairly high survival rates with about 65% estimated to reach adulthood.

Another study by Bosch and Vicens 2006 of the mason bee Osmia cornuta over several years reported an average of about 10 eggs laid per female, and similarly low mortality rates. Unlike tarantula hawks this species does at least lay multiple eggs in one nest, but must make many trips to collect pollen, nectar, and building materials, taking about two days per offspring on average.

In contrast, a more "r-selected" species like a monarch butterfly may lay many hundreds of eggs in her life, but mortality rates are typically above 90% (Zalucki and Kitchling 1982).