Telescopes and any other optics that look at objects in space are set so that the focus is at infinity as defined by the equations of optics.
Resolving power has to do with the size of the primary mirror and the wavelength of light that you are interested in. The smaller the mirror, the less angular size you can resolve (so you can only separate two objects that are far apart). The bigger the mirror, the closer two objects can be and you can see them as separate features. Similarly with wavelength, the longer (redder) the wavelength of light that you're interested in, the bigger the mirror you need, whereas the shorter (bluer) the wavelength, the smaller the mirror can be. This is known as the diffraction limit.
But there's another factor to consider, and that's the resolution of the actual detector. Let's say that your diffraction limit for 500 nm light (green) on a 2.4 m mirror (Hubble) is roughly 0.05 arcseconds. But, if your detector only records 1.00 arcseconds per pixel, then that is your limit. Usually detectors are designed to be at or a little better than the diffraction limit of the optics, though.
In terms of time needed, that has to do with how bright the object is per angular unit. For example, the Andromeda galaxy is very bright as a whole, but that brightness is spread over a large portion of the sky. So the brighter the object is and the more concentrated that light source is, the shorter time is needed to properly photograph it. And this also has to do with the "speed" of your optics -- a larger f/number is "slower" and requires more exposure time than a smaller f/number.
But every detector is different in terms of how sensitive it is and how long you actually need to record the same amount of light. This gets into issues of quantum efficiency that I think are beyond your question. Suffice to say, there is no set equation to know how long you need to expose an object to properly capture it.
It depends on what you mean by "view." If you just mean "see" a spiral galaxy, then you can do that without any telescope: the Andromeda Galaxy is visible naked eye from a good dark sky site. If you mean "see detail" such as spiral arms, I'd say the minimum aperture is around 10 inches (250 mm). Although you can occasionally glimpse spiral structure with smaller apertures—I've seen the spiral arms of Messier 51 in a 150-mm refractor—10 inches is the minimum to see structure in galaxies routinely.
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Sort of.
As Space.com writes,
As an interesting aside, the Wide Field Camera 3 sees in wavelengths other than visible light, as do the Cosmic Origins Spectrograph and the Space Telescope Imaging Spectrograph.
NASA goes into a litte detail about the process here, as well as some of the rationale behind choosing some colors. Some of the reasons for using artificial colors include showcasing elements whose emission lines are out of the visible spectrum, and showing features that are too dim at visible wavelengths. Remember, CCD detectors usually don't see the same things that humans do, and Hubble can see outside the visible spectrum.