Why can you get banned on your main Xbox account for something you didn’t do? Should there...

Any information regarding your ban would be listed on the enforcement site. http://enforcement.xbox.com Even if you didn't say anything, you are responsible for your account at all times. So if your sister said something while using your account, you can get a ban. Spam reporting does not result in a ban. A suspension can be given for 1 valid report. The enforcement team do not iasue bans based on a quantity of reports.

your main account might be banned, can you get on xbox with it?

you do not get banned for cheating, only get the score removed and branded cheater, now if you mod an account after a reset THEN you get banned. the PET who handle all enforcement on accounts do not do the reset and cheater watermark without 100% proof that
any of the scores were earned from non legit ways. you can post in the my account was suspended section on the lower part of the forum main page but they will just tell you why it was reset and they do not reverse it and there is NO appeal for it, the only
way to get that score back is to create a new account and start over. if it was not you who modded the account's score it does not matter your account is your responsibility at all times so even if somebody does something to it you take the fall, sorry.

You Can Go Ahead And Contact Xbox Support In Regards To The Account That's Banned But I Cant Promise If Your Account Will Be Unbanned As Some Bans Stand But Anyways , They Should Be Able To Do Something To Help You Out.

That's sucks! But MS owns all rights to xbox live and what they do with it! If they don't like something they can ban you for it and nothing you can do about it! All you can do is stop giving them your money! They don't even have to give you a reason why
they banned your accounts!