The sun is getting fainter right now, and we are noticing that the Earth is cooling off in the last couple of years in response.

You are absolutely right to be thinking about global warming and sunspots. In addition to the 11-year cycle, there also appears to be a 2-300 year cycle as well. This longer-term cycle was probably responsible for the Little Ice Age, a cold period during the 1700s. It is very possible that much of the observed global warming may in fact be just the sun getting brighter over the past two hundred years. However, things are also happening that indicate that climate is doing things that it hasn't for many thousands of years - the glaciers on Kilimanjaro disappearing, for example (those glaciers are many thousands of years old). Still, how much of that is our doing, and how much of it is natural? I think I can confidently say that nobody really knows yet.

I might be wrong, but I think we're near a peak in the number of sunspots. Sunspot cycles have definitely had an effect on the Earth's climate in the past and could do so again. There was a period of time called the "Little Ice Age" several hundred years ago that coincided with a minimum in solar radiation.