Conventional physics as is usually presented in textbooks deals with the evolution of states in phase space parameterized by sharp instances in time, a real parameter. However, quantum fluctuations seem to suggest we have to smear a little over time to average over vacuum fluctuations and the like. What implications does this have over the meaning of 'now' and the nature of time?
"Now" includes certainly a finite period sufficient for collecting some data. It is like an exposure time of a frame in a movie. Too short exposition period leads to dim and "uncertain" frames (information). Too long one piles up too many events. So the instant "now" is an idealization of reality, which is different in different circumstances.
You need to discuss the "now" of a particular physical system. For example, if you are listening to a Geiger counter, is "now" when you hear the detector click? When the detector itself clicks? How about when the current reaches the critical value to trigger a click? The initial event sparking the click?
You're running into a question of quantum foundations, so you're not going to get a canonical answer to your question because there isn't one. The question really becomes, what are you trying to predict? That will determine the way you build time into your theory. The model must be driven by experiment, not the other way around.
An answer you might find more satisfying: in quantum field theory, time is treated much like space in that there is a single real variable giving the "proper time" of the system in question. The measurement is then modelled with the "time-smeariness" you are looking for.
An implication is that you can borrow an energy $\Delta E$ during a time interval $\Delta t = \hbar/ \Delta E$. This allows for interactions mediated by massive particles, as they can use this time to travel up to a distance $c t$ before Nature, or the Market Forces, ask the debt to be paid.
It is well known in algebraic quantum field theory circles that for interacting quantum field theories, you have to smear over time to regularize. This rules out, one might even say refute, canonical approaches. Sadly, this is hardly known outside AQFT circles, and people blithely continue to use canonical quantization. Only the covariant spacetime approach survives.
One of the less common interpretations of the relationship between position and wave in quantum mechanics is that the wave is the ontological description of the situation in the future, while the particle description is ontological for a situation in the past. Then the correspondence principle is the action of "now" on the wave function that produces the result of a measurement; the particle positions. Thus before we run the experiment we represent it as a wave function. After the experiment is ran we can think of the waves as particles.
This is in the literature but it's not common. If you're interested I can dig up a link to an arXiv article or maybe more.
Yes. But the reason is completely independent of quantum physics.
The notion of "now" determines the time only within an uncertainty of the order of the time it takes to say or write the word.
Similarly, the notion of "here" determines the position only within an uncertainty of the order of the size of the speaker or writer.