i will respond to your other questions when i'm able to sit down and type out the answers but i really, really, REALLY like touhou so i needed to get this answer out as soon as i can. hopefully this is a good guide to help you out a bit

the touhou series thrives off of two things primarily: the games themselves and the FUCKTONS of fan content there are. the former tend to be hard as balls, as expected of bullet hells. you have two possible starts: the FIRST game, Highly Responsive to Prayers which is part of the PC-98 era up until Touhou 6: Embodiment of Scarlet Devil, which is the second place you can start since it's essentially a reboot of the entire continuity. there are fangames you can get stuck into as well—touhou luna nights is one of the best ones you can buy—so you don't hafta stick to the official ones if the difficulty is too much for you. i, personally, actually played the gacha game (Touhou Lost Word) since launch until around about december last year, so that's an alternative route you can take if you want that instead

however, being completely honest, the games themselves do not feature character-heavy interactions like you tend to see in fanart or writing. the fan content is what tends to define the interpretations of most characters, whether it's music or fanart that has a character acting a certain way. genuinely the best way to get an understanding of the characters is through the fanart because it's easily accessible and most interpretations stem from the fan content anyway. yes this does mean that TECHNICALLY you can just read fat porn of the touhous and you'd get ONE of many fan interpretations but you know what i mean

also a choice you can take are the mangas, which are canon. i read Silent Sinner in Blue and it was really fun (and focuses on the Lunarians, which are my favourite group in the whole of touhou), so if you wanted to take a third option and do that instead then by all means please do go ahead and give it a try. i hope that this answer helps you get a good idea of what you want to do