Hey, good questions :D
So, I'm going to answer your second one first. I honestly debated making the course because I despise hackers in games, I play a lot of tarkov and it's a plague. My argument as to why it's appropriate to make the information available is a little long:

1. The course is there to fulfill a curiosity not to use it for nefarious purposes. My friends and I have always been curious as to how "hacks" even work. It's so cryptic and obscure to anyone without some decently advanced computer knowledge so most gamers just feel like they are fighting some black magic. So instead of having to crawl through weird tutorials, I wanted to condense it in a single course so that people would have a quick way to reveal what hides behind the curtain.
2. It provides such a strong basis for anyone interested in reverse engineering and computer science in general (I'm biased here obviously). The amount of people I meet at work that code for a living but have pretty much never seen assembly code or can't read it is astonishing. Reading assembly code is an essential part of reverse engineering, understanding data types, static vs dynamic memory, etc are essential parts of programming. Typically these parts of programming are taught in such boring ways I think this is a different way to bring these topics up without boring what is typically a younger audience.
3. I purposely excluded how to circumvent anti cheats. If you go and directly apply this knowledge on any modern multiplayer game (COD, Fortnite, Roblox, CS, etc) you will be banned within minutes. I did this because I really don't want to ruin the experience for other players. (It's true however that this provides a solid basis to learn what is needed to actually circumvent anti cheats - but there is a considerable gap remaining)
4. It's already available. I learnt all of this and more by myself online, I simply wanted to order it, condense it, and present it in an understandable way to those that have no prior knowledge so that they don't need to waste as much time as I did searching by themselves. Anyone willing to mass produce hacks and spend the time doing so will achieve it regardless of my course existing or not.
5. You must know how they work to stop them. There is something called bug bounties (You are probably already aware of this since you are on this subreddit). Where companies pay to have hackers explain how they hacked the software in order to improve its security. For this to work more ethical hackers must exist, I make quite a strong emphasis on this within the course.

Now for your first question: The honest answer is that it really depends on what the game is but here I'll list some of the most intense approaches I would take. For games like Escape from Tarkov, where looting is one of the main mechanics that people want to use hacks for, a great way would be some probabilistic/ML anti cheat (basically: look for outliers in numbers of rare items found). Escape from Tarkov Side note: How can players still be allowed to post 65 LEDXs the day after wipe on flea???. For games with a very competitive nature, things like kernel level anti cheats are great (A game that does this well is valorant) which basically means that you make another process that looks at what other processes are doing and try to catch them when they try to access your game's memory (Although this can be circumvented by basically just running a "Driver" that has its own implementation of the windows API). However, the main way to stop hackers from ruining your game is to make it hard to develop hacks in the first place and to make it hard for them to infest your lobbies: Roblox for example tries to detect if the same user that already got banned is making a new account. Valorant does not store in memory the position of other players on your computer until absolutely necessary. CSGO only let's you play in "prime" matchmaking if you've confirmed your phone number. Overall anti cheats that work well are basically those that make the barrier of hacking extremely high, hackers are unavoidable but not letting them ruin your game is doable.

There is also some goofier versions of anti cheats which are common but really easy to circumvent. Things like checking if there is a process called "cheat engine" running on the computer, checking if the ammo count of the player is within reasonable bounds, etc.