Yeah you can say that, we use this sentence now just to show you are welcomed.

Yes it is. However, it is old fashioned to say that in informal conversations.

In my opinion, 朋refers to a man who has a same aspiration as yours. So here 孔子 was probably talking about the value of the collision of ideas instead of the simple socialization. 《说文解字》讲，朋为"共修仁义"者。 If you want to understand 孔子's ideas fully, you'll need to truly understand the meaning of "仁", which can never be fully translated into English.