Not really. You can say „proszę” for example when you urge somebody to get inside or as a reply for thanks ("You're welcome"), but not really as a welcoming phrase.
'prosze' works the same way, actually. Inviting someone to your house, that's the word you would use.
Only in some contexts. That is literally I/We invite you, so it won't fit every situation... it will when someone enters your house or restaurant, it won't when you want to say something like "Welcome to Poland!"
OK, we can accept it here, where there is absolutely no other context, and for "Yes, welcome!", but generally it's an a bit problematic translation...