Dzień Dobry means Good Morning not Hello. Welcome I have no idea whenever you mean welcome as a noun or just as a greeting word. Cause "powitanie" is a noun. But if you meant welcome in a "Welcome, come in" style it should be Witaj or Witajcie (plural form).
Also I am might as well be "Ja jestem" and You are "Ty jesteś"
Also I am might as well be "Ja jestem" and You are "Ty jesteś"
Random might as well also be "losowy"
niesamowity
wspaniały
cudowny
wyśmienity
świetny
etc.