Canonical Ensemble

First, small or large has to be determined from a relative point of view. As long as the system much smaller than the reservoir, then the variation works fine and it is ok to ignore the higher order terms, giving us the standard $e^{-beta E}$ factor.

Second, strictly speaking the number of degrees of freedom should not be directly related to the size of the system. However, in order for the reservoir to have sufficient contact with the system to act as the heat bath, then the size of the reservoir probably shouldn't be too small from a practical point of view.

1. What you do for larger systems is enlarge the reservoir until it dominates. The expression one obtains is then valid in this limit. The very definition of the word "temperature" involves this idealization.

2. The reservoir is a fiction introduced for the purpose of calculation. One could indeed use a physically large reservoir, such as the Pacific Ocean or something like that (with devices to make sure any heat exchanged is also rapidly conducted throughout the reservoir), but one could equally well use a small entity equipped with a thermostat. The thermostat has the job of making the small entity stay at the same temperature, no matter how much heat it exchanges with your chosen system. The claim is that the system will not care about exactly what is going on inside the reservoir, so the calculation based on a physically large reservoir also applies to this case.