Are there any optional rules in D&D 5e concerning bonuses to attacks per round for characters with higher than average dexterity scores? It only makes sense to me that a fighter with a dex. of 17 would be able to wield a melee weapon at a higher rate of strikes per round than a fighter of the same level with a dex. score of 8.
But remember: a single attack in Dungeons and Dragons doesn't necessarily correspond to a single strike with a weapon - just a concerted effort to inflict harm to a target with a weapon. While it's possible to imagine that combat involves characters and monsters facing off for a few seconds, then each making one strike, and then settling back to a staring contest while they wait for the next combat round to start, that might not be appropriate if your campaign isn't based on a Kurosawa movie. A high strength character's attack might be a single mighty swing, while a high dexterity character's attack could be a series of rapid jabs.
Nope. You only get one attack per action, unless you have the extra attack feature. You can also make additional attacks with your bonus action if using light one handed weapons (can be improved with class features or feats). No amount of dextery will affect your attack options if you are going by the rulebooks.