Welcome is a verb,
We welcome you to Rio de Janeiro
They welcomed the good news.
When we arrived, we weren't welcomed
and a noun.
What a lovely welcome.
The cold welcome was unexpected.
Welcoming is an adjective
His cosy home was very welcoming
The people of Rio are so friendly and welcoming.
Oregon is one of the most welcoming states for incoming refugees
as too is welcomed
The sunny weather provided a welcomed change.
A larger size would be very welcomed.
And welcome is also an adjective,
Welcome to Rio di Janeiro!
You are very welcome to stay the night
Sam is always a welcome guest
Collins Dictionary has a very good page about the different uses and meanings of welcome, and says
under no obligation (only in such phrases as you're welcome or he's welcome, as conventional responses to thanks)
But offers no insight as to why WELCOME and not WELCOMING or WELCOMED is preferred. Is there a grammatical reason for this? Is it down to convention and idiomaticity?
Q1: Should I always mark “You're welcomed” as wrong?
Q2: Is the full form “You are welcomed” better, more acceptable?
I am not a professional or qualified teacher but I do occasionally give private lessons to Italian students of all ages and levels. A private asked me this yesterday, and the best explanation I could come up with was that English native speakers have said “You're welcome” for over a hundred years, so it is perfectly grammatical.
The following questions on EL&U are closely related, but they did not ask “why”. Consequently, the answers posted either ignored the issue totally, or failed to address it in any depth.