Hi. I'm new to the community, I started speedruning this game 1 month ago at most, I've been miss-splitting very often and I want to know if I need to save all my splits no matter what or I'm free to delete them all and start new splits whenever I want or need?

I'm asking because I don't want to look bad by submitting a run and then on my streams have an empty LiveSpit or submitting another run with an empty or completely different times on my LiveSplit.

You actually don't need splits at all for verification.

If you have a suspicious looking run for any number of reasons, a full splits file can help provide evidence in your behalf, but it is not required.

I'd save the old splits files regardless since they hardly take up any hard drive space, but certainly you can start fresh on a new file.

If you play on emulator, you can use the autosplitter in https://www.speedrun.com/smb1/thread/vi46e so that you don't have to split manually.