The data set in question is the one that is historically chronologically complete, in the sense that there are daily records from one location that can be compiled together. Before the 1880s no one was keeping regular temperature data so everything before that has to be inferred with other scientific techniques like ice core samples.

So, the answer to your first question is realistically and statistically, no. It is not a large enough data set to draw conclusions from, since this a sample from one place for 140ish years and climate happens all over the globe from the present all the way back to you know the foundation of the planet. Trouble is, this graph can be drawn from location points all over the world with similar windows of time. This is just the longest one with this type of granularity, so it gets used all the time.

I don't know how the average/mean temperature for a day is calculated, if 24 points were measured every hour and averaged out for a day or what. I'm sure you could find out this info with some google fu.

I'd recommend the XKCD comic on earth temperature. It gives you a long enough time line to understand the enormity of the change we're experiencing right now.

Thanks for taking the time to clarify your question. Have an up vote :P