Capacitors

Unless you have specs, I'd never replace with lower voltage cap, there is a reason certain voltages chosen. You can replace lower voltage with higher voltage, may or may not be a reason for this.

Yes, but depends where. 

In tube amps and preamps is the only place where you are likely to actually run into this scenario.  In signal, as opposed to AC filtering, so long as you keep a 25% margin, get the smallest that’s appropriate.  

So if you have a signal that is nominally 300V then anything 400V or more is fine. 

However, in an AC power supply filtering applications having a cap which is higher than the peak of the AC waveform AND is intended to be a smoothing capacitor (i.e. used with pulsing DC)  is critical.   A cap which is not will short in minutes because the current, not the voltage, will cause overheating.

Just as background, film caps often can't get smaller than a certain V just because they are too hard to manufacture.  So your smallest V choice may still be greater than you need.  In speakers for instance, anything over 80V is fine, but I can't really find a film cap less than 400V

PS - DIYaudio is a great place for questions like this and has a bunch of friendly builders and modders who would love to help you out.