What the heck is with all the no's? D: People should be posting if they don't have the game to speak for themselves...
You can see all the pokemon without trading. You need to need to talk to this lady, and she'll show you the picture opposite of the pokemon legend you got for your game. That's the only Pokemon you can't see on your own by battling/wild encounters/legends.
I'm not sure who gives you the national dex, but both of the prof. are there, and you get it when there...so... D: I don't really think it matters.
As for "different towns" I'm going to say no. Why? Because I personally tested to see if you can get to 'battle island' with just the national dex and not beating the E4, and you can't. There are some weird restrictions once you get the national dex and not beat the Elite Four, but I won't bore you by that since that's not part of your question.
The only 'extra' spot you get with just the national dex and not beating the E4 is Pal Park. Though, as the others said, you get to go to Battle Island once you beat the E4...