I would like to know if Laybmod 3 can see my Minecraft password, I did not specify my account details with Labymod, but my account and my e-mail address are still there without me giving them!
No. The password can't be seen by LabyMod. The email address but already and theoretically LabyMod could see your login token and thus give the mod developer a free (temporary) account. By that I mean the following: If you have a login token then you do not need a password or an email to log in to your account
PS: A login token is not valid forever. He will eventually be regenerated