Map making for source engine games
Map making for Halo: Custom Edition
Where to get maps/tags?
http://hce.halomaps.org/
https://haloce3.com/ce/
To play a Single Player map, open console and type: map_name my_map
Level/mod making for Skyrim
Where to get mods??
https://www.nexusmods.com/skyrimspecialedition/
https://www.afkmods.com/
https://tesalliance.org/forums/
https://www.fliggerty.com
Making a level for Doom
Doom is the easiest game to start with. You want to install SLADE and Doom Builder 2 or Ultimate Doom Builder. Use ZenNode for building nodes. I recommend making a Boom map first.
Where to get WADs from?
https://www.doomworld.com/idgames/
https://www.wad-archive.com/
https://www.gamers.org/
https://www.moddb.com/games/doom-ii
https://forum.zdoom.org/
>Is it possible to make half life 2 maps without buying half life 2?
No, because nowadays Hammer is distributed with the game (IIRC, "runhammer.bat" in the game folder). BUT you could map for CS:GO or TF2 (which are free).