When you are inspecting, you need to have a reason (or several) in mind for the inspection. In Spring and summer, it will not only be hive health and brood pattern, but also whether the colony is making swarm preparations. That means looking for queen cells. If you want to prevent swarming, you need to inspect every week. You can get away with 2 weeks, but you may be too late to change their minds at that point, so it can be risky.
In autumn and winter, you may not need to inspect much at all, depending on your climate. If you have year round nectar flow, you will have to continue with one to two weekly inspections. If it gets cold, all you need to know is how the food stores are doing, and whether you need to feed the bees. The less inspecting you do in cold weather, the better.
Eggs hatch into larvae, capped pupae “emerge”. Good for you for asking though, 99% of beekeepers (of those not in this forum) don’t know the difference.