I understand that in the medieval period of plate armor, the effectiveness of swords was limited. How often were arming swords and long swords used in this period?

I think it's important to remember that armor was never common during what people commonly refer to as the European medieval period. It's far too expensive and often has to be customized. Armor was limited to either lords, commanders, or very elite troops. Plate armor especially. The vast, vast majority of your opponents on a battlefield were likely to be ordinary unarmored soldiers.

As to dedicated swordsmen, well, think about who has time to train. It's not the ordinary peasant. There were very few standing armies at the time, and anyone who can afford to train in swordsmanship can afford other weapons and additional training in them. So no, there were no dedicated swordsmen, as such. Most knights had multiple weapons, including specialized weapons to deal with armor.

As a side note, swords can be deadly against armor. Surviving manuals on swordsmanship demonstrated many alternative methods of dealing with armored opponents besides the standard thrust and slash. The "mordhau" or murder stroke, was one such technique that involved holding the tip and edge of the blade and using the blunt pommel and crossguard as a hammer.