First: You don't get punished for false reports.
Second: If you want to talk to player behavior specialists, open a support ticket
Third: Remember, the forums have no power to undo any punishments. The most we can do is help you understand why you got punished. You have to open a support ticket to get anything fixed with your punishments.
Fourth: You claim that you were punished for racism, but you don't show us the actual text of the punishment notice. Riot does not really specify that you were racist in the reform cards, they just say that your speech fell below the standard of the community and you are being punished for it... which means you are guessing you were racist but not sure... or you are just making that up to get sympathy from the forums... or you've modified your chat log to exclude certain lines. This is also a reminder of the third point, trying to get our sympathy doesn't help you. Riot player behavior specialists are the only ones who can help you change a wrongfully issued punishment. If the punishment is rightfully issued, it won't get reversed.
Fifth: Asking for a player to be reported in and of itself is not toxic enough to get punished. However, if it's bundled with harassment, flames, etc... then your harassment and flames get viewed even more negatively because you asked others to report them. Reds have posted this MANY times. You just need to search through the red posts. Additionally, reports are not tallied by number. If there are reports, a game is reviewed regardless of how many reports, so ultimately asking other people to report is pointless and also self defeating.
EDIT:
Sixth:
{quoted}
Game 1
In-Game
HashTagGoodGame: how to counter pyke cc him after he goes in boom he's useless he has 0 escape after he e's
HashTagGoodGame: stop fighting bot lane
HashTagGoodGame: stop fighting
HashTagGoodGame: and you went in
HashTagGoodGame: i watched
HashTagGoodGame: cause you already fed them nine millian kills the game is over
HashTagGoodGame: you are the carry and are doing nothing but fighting and dying in bad fights
HashTagGoodGame: keep talking the more you say the more likly the report results in a ban
HashTagGoodGame: gg
You're arguing here and starting to flame them. This is the beginning of a downward spiral. You should have muted them here and just played the game, but instead, you continued to engage.
HashTagGoodGame: i had like 100 hp
HashTagGoodGame: not dying on a stupid fight that's why i back up
HashTagGoodGame: and lucian shows up with 10 kills and kills everyone
HashTagGoodGame: please report bot verbal and inting
This is pointless. Not only did you ask for a report (see point five) you are accusing them of inting. You're starting to escalate your flames.
HashTagGoodGame: it's all in chat
HashTagGoodGame: ?>
HashTagGoodGame: fun gameplay
HashTagGoodGame: i have 4 deaths and you?
You're insulting and flaming them. You really need to learn to disengage.
HashTagGoodGame: and they have happened to lucian all of them because bot ran face first into them all laning
HashTagGoodGame: except i won't
HashTagGoodGame: because i've done nothing wrong
HashTagGoodGame: this account has never been banned since season 3
HashTagGoodGame: the review all reports
This is true, they do review reports, and as far as I can tell, you kind of do deserve a chat restriction.
HashTagGoodGame: so good luck cause I did nothing wrong
HashTagGoodGame: gg please report top bot and support they are a premade just flaming threahtening me with reports when they are toxic and inting they said so in chat they don't care and are swearing a lot
Again, you kept asking for reports and it's bundled in with harassment and flaming.