Fiora is a lane bully. Her Q having good early damage makes sense.
Her E speed boost is unreliable, since she needs to attack to trigger it. It's great for chasing, but if you're trying to escape, you have to stick around long enough to land a hit or two first, making you vulnerable. In addition, since it's really only a soft disengage (and she can't use Q to escape unless there are nearby enemies) she's highly vulnerable to slows.
Her ult does have counterplay, albeit in limited options. Zhonya's lets you ignore her ult, as does Jax's block (I think another Fiora's parry might also block it, since I think it's coded as a basic attack). I'm not sure if QSS affects her ult.
In addition, Fiora deals only physical damage and is highly auto-attack dependent, making armor items (such as Thornmail and Ninja Tabi) highly effective against her.