I will actually address your questions as best as I can b/c the way you phrased everything seems more opinion than fact.
Nasus's slow is single target, so is SS and pretty much his ult. His kit is built to duel. If you are fighting Nasus 1v1 then eventually you will lose unless you have the sustain, true damage or pen to kill him. Fiora, Darius and most ADC's can accomplish that if they do not lose lane and can scale either off Nasus or off another lane.
Nasus's build really doesn't incorporate any natural attack speed items. He gets bits and pieces of things like that from Trinity but nothing else.
His healing is purely dependent on how many stacks he has and if he can fight you inside spirit fire. If he lacks stacks then he barely heals, if you don't fight him inside spirit fire then he can't penetrate higher armor to heal. His heal can also be severely crippled by cheap items like Executioner 800g or Bramble Vest 900g. Ignite or Morello's also kill his healing and that is huge part of his defensive capabilities. Without his healing he falls very quickly to sustained damage.
The point about towers is irrelevant. Most ADC's or AD Melee carries can shred towers much faster than Nasus can. Tryn, Yi, most ADC's for example shred towers insanely fast. This is more an issue with tower balance then anything else.
Your goal should be to pick a champion who is better at lock down and team fight. Don't bother trying to win the lane you are in as much as the game.