Your use of not using "to" before "home" as it is an adverb is correct, as well as your second statement. That use of "You come to home" is really, really strange and I've never heard that before. It seems to be a typo. I would say "You come home and you want to tell your brother what your friend told you." Either that or "You come to your home...", though the first one is much more natural.
Anyways, to answer your question, here are a couple of SE posts!
https://english.stackexchange.com/questions/33652/why-is-to-not-used-before-home
This one details how the word "home" functions in several ways (how it can be either a noun or an adverb).
Can we use "to" before home, if we are using determiners (her, my, your etc.) before home?
The second explanation is very, very good. It details how "home" acts when bare and surrounded by other things.
I hope this helps, and feel free to ask if you have any more questions or if I didn't answer properly! :)
I'm a native English speaker, from the Midwest (US), if that counts for anything. There are variances in language, so if this is a regional thing, I don't know about it and I apologize for that.
Take a flying leap (off a bridge)
is a colloquialism telling someone to go away or get lost and hopefully never come back
Other ways of expressing the same message are
go curl up in a ball and die
take a long walk off a short pier
Got a dime? Go tell someone who cares! (when payphones were more prevalent)
Best Answer
No. A typo is a typographical error:
American Heritage Dictionary "typographical error"
"A mistake in printing, typesetting, or typing, especially one caused by striking an incorrect key on a keyboard."
A typo is an error in spelling, that is, an incorrect letter or symbol.
Being bumped by another person when you are writing can't make you produce an incorrect letter. It will probably result in a smear or scrawl.
(The OP asked specifically about "writing something down". That phrase means to make marks on paper with a pen or pencil, and doesn't apply to any sort of typing.)