1. There's no way a katana could get through Gothic Plate. To get through such armour you need to thrust with the tip of your sword and the opponent needs to be prone so you don't just push him away. Katana's curved blade makes it quite unsuitable for thrusting, so you'd have a hard time using it against a well-armoured opponent. And curved blades are designed for use against unarmoured opponents because the cleave flesh better than straight blades. It's the straight blades that have the edge when it comes to hacking through armour (though neither are very good at it). This is why straight swords were popular in Europe where armour was also popular, and curved swords were popular in the Middle east where the climate prevented people from wearing much armour.
While I admit that saying a katana can slice through anything is a bit overexaggerated, I've seen them do some impressive things before. And yes, I know a bit about swords.
Also, katanas are very, very pointy. I'd hate to see what would happen if someone in steel plate (traditional steel, at least) came up against a properly-made katana. Maybe nothing, because I haven't seen it, but I think there's a good chance of some serious spleen-piercing.
2. Nodachi is two handed. Katana could be wielded two handed, but it as more common to wield it one-handed and use the other hand to wield a wakizashi.
Study kendo; it is based on traditional katana techniques, and there's a lot of two-handed attacks in that. The wakizashi is an almost exclusively thrusting sword, more akin to a dagger than anything else. The 'parrying blade' you refer to later is actually the kodachi. (Lit. 'small tachi'; 'small sword')
3. I assure you it's go nothing on the zweihaender when it comes to this last point. Fighting with a zweihaender was a very risky business as you couldn't carry a parrying blade and the wide swings could leave you wide open if you didn't know what you're doing.
The zweihaender is an exclusively two-handed sword (as implied by the name). Are you trying to compare a massive beast of a weapon to the three-foot katana? I hope not.
In conclusion, I think that all katana has going for it is good PR; Damascus and Toledo blades were made of superior metal and their design was at least equally as good as katana's design, if not better.
Superior metal, yes. Equally good design, yes. However, superior metal cannot compare to differential hardening, tamahagane aggregate, and the time-honoured technique of multiple folding.
Seriously, at least learn as much as you can about
real katanas before you badmouth them.
I've got that out of my system, so I'm willing to be a bit more reasonable now.