Maybe this is a cultural difference, but i would generally consider it incredibly rude for a random person to interupt someone trying to enjoy their meal. A resturant isn't a singles mixer.

Depends on the layout. If its a large, sit-down restaurant with wide gaps between the tables, then yes it would be weird for me to go up to you and say "Hi, Stranger!". But at a coffee shop you might be sitting right next to me. We might even be sitting at the same table waiting for our food. Am I not allowed to talk to the person sitting right next to me? I ordered some food the other day and realized there were no free tables, so I asked a stranger if I could sit at his table and had a conversation with him and his buddy.