The "Mein Mantel ist kurz" and "Mein Mantel ist groß" sentences are very similar and misleading
My coat is large/small is misleading? They're two different sentences with different meanings.
Why does Gross mean large but not big?
In general groß means also big. It depends on the context if it should be accepted or not. Here it's fine, I think. I would probably call it a large coat.
It can be both, and when describing a person, it usually means TALL!
I cannot tipe that letter