I am not a good player and even less with Mario, so I'll let other more experienced players correct me/elaborate more.
1) Can you do all the advanced techs? Short hop, z-cancel, short hop double aerials, etc?
2) The tornado is useful for recoverying. If you mash B really fast Mario will rise significantly and that helps you recover. Do it from afar (before using your second jump) as the ending lag makes it easier for your opponent to hit you. Other than that, it shouldn't really be used and it's more a gimmick than anything else. Since it comes out really fast it could be a good defensive option, but Up B is as fast and is better to get you out of dangerous situations (escaping pseudo-combos).
3) Shielding is most of the time bad in smash 64. The huge amount of shieldstun makes for a lot of guaranteed aerials into grabs. Your defensive options are also reduced while shielding. I'm not sure what you mean by "shield demolished", but if you mean shieldbreak, then that should never happen against Pikachu. Even if you shield on accident (or because you didn't know what else to do), you have plenty of time to usmash/upb/roll/etc as Pikachu tries breaking your shield. Pika's best bet would be to grab you anyway in that case...
4) Pikachu's neutral B should never be a problem in any matchup. The fact you struggle with it hints me that you're probably still a beginner. To avoid those neutral B, you can short hop above them, go onto a platform, hit them, or even shield: they are so slow (as in Pika's ending lag is so huge) that even if you shield you'll be safe. On the contrary, if you're close enough you should even be able to punish Pika.
5) Fireballs are a lot better than Pika's neutral B. Mix up between short hop and full hop to fireballs. Full hop fireballs into grab can be an easy and effective strategy.
6) The metagame is defined by the players who play the game, so it's hard to say why the Japanese believe so. Keep in mind that it is a different game too. And even here, some people (Star King for example) are starting to believe Jigglypuff is better than Mario.
All in all these are really really basic tips, because as I said, it looks like you're a beginner and that your Pika opponent isn't really good. Again, if you could provide vids we could help more specifically.