Yuzow, something I did was print out inspection sheets where I would fill in what each bar "had" and thoughts for next time, etc. Usually I fill it out after the fact because I can't inspect and write!
On the bottom I added the days it takes a worker to become capped (9), to emerge from the cap (20), and then to mature enough to out and forage (40 or so). If you look at those days, it takes nearly a month for a drone to go from egg to flying. So if you are seeing drones at your hive.... they did not come from your queen. This is very exciting! it means that you have a feral (or managed) hive nearby! Drones apparently have a habit of finding "any port in a storm" and are not too picky about which hive they go into.
About inspections - it is harder to move fast, especially at first, and the longer you take the more stressed the bees can be.
First, I'd say watch this video by Randy O - https://www.youtube.com/watch?v=OcfqTx4_FAo - he talks about what it takes for the bees to become defensive. When I inspect, I try very hard to avoid sudden jerks, bangs, or quick large moves. It makes my inspecting slow, but I don't have too much trouble with the bees become defensive - until I get to the brood nest. It's typical for my one hive (feral lineage) to have a handful start headbutting about the second bar into the brood nest (so maybe the 15th bar). That is as aggressive as they get. I have heard of bees covering the veil and stinging goat skin gloves - haven't seen that yet thankfully!
Second, you can set your hive up so you either go in the front/brood side first, or go into the back/honey side first. My entrance is on the narrow side, so I have set up an empty bar at the front so I can go into the broodnest first, so that helps reduce the time it takes me to get to the brood nest. And reduce the time I need to open the hive to get my questions answered. BTW you should not have many entrances - just one - like a bee tree. Otherwise your bees are vulnerable to being robbed by other bees. This will make them cranky.
Third, I make sure I rehearse my purpose before I go in. Is it to check for eggs/brood? Then I can go in the brood side. Is it to check their stores, or add space between honey and brood areas to reduce the urge to swarm? then I go in the honey side. I do a full inspection at the beginning of the season, but then I will just do partial ones.
Good luck, keep working on your technique. It will get easier!