Keep in mind if you are a female, il faut dire: "Je suis bonne"
so bon is for masculine and bonne for feminine?
yes, bon is masculine and bonne is feminine - both in singular.
in plural: bons and bonnes.
and why when I write "je suis bonne" duo said that was correct?
"je" is genderless (as well as tu, nous, vous), obviously the agreement will be made according to who is speaking.
What does "bein" mean?
"Bien" is usually an adverb, while "Bon/Bonne" is usually an adjective. You can read more about them here: http://french.about.com/od/grammar/a/bon-bien.htm
Do you mean "bien"? It means "well".
Unclear English phrase. «Je vais bien» if in reference to how you are feeling.
«Je suis bon à qqch» - «je suis bon» dit que «je goûte bien»...ce semble sexuel.
My French speaking friends tend to respond with "ca va bien" rather than Je suis bon/ne