Response time? No. It's not that simple. No simple number is able to describe everything related to what response times are. However, if you want to give vague comparisons of two monitors, pixperan should be fine. It has a number of tests you can perform that relate to related things and you can find many other results online, allowing you to somewhat compare your monitor to others.
Refresh rate? Quite often, 3D applications as well as your display settings in windows are enough for that. It'll tell you what your GPU is sending out to the monitor. If it says 120hz, that's the signal you're sending to the monitor (with a few rarer exceptions). On 120hz TV sets, which are not true 120hz, you can mostly only select 60hz and the TV will use a method of filling out additional frames in between. Some monitors include some place on the OSD where you can check the current resolution/Hz, which is rarely inaccurate. If the two of the above = 120hz, you're pretty much guaranteed to be running at 120hz.