I'd love to play Gronkh's After Humans Modpack and know that I need version 1.7.10 of Minecraft for that. Do I still have to buy the new Minecraft version for 24 euro in the shop or is there a different way for the older versions?
And if I bought then the newest version how do I indicate that the Modpack should use the older version?
If you buy the game you can play all versions. Of course, there's another way, but it's not legal.
No, you do not have to, you can play Minecraft for free with a Cracked Launcher, but with the disadvantage that you can't join almost any server.
The Cracked Minecraft player base is not very big compared to those who bought the game, so it will take a lot of effort to install the After Humans Modpack.
If you buy Minecraft (Java Edition), you can also easily select older Minecraft versions in the Launcher or even install other ones, such as Minecraft. Forge what is necessary for modpacks.
Of course you have to buy a game if you want to play it. Basically, you only buy one account that has Minecraft eligibility. In the Technic Launcher you sign up with this account and then you can download After Humans there. It could not be simpler.