How to analyze a dB graph?
How many minutes in total are above 60 dB?


You can't tell that from the graph alone. 

Loudness can change many times in a second, and one of the pixels in your image is 24 seconds long – and you're not specifying whether "minute above 60 dB" means that a single instant in that minute was above 60 dB, or the average loudness in that minute, or somethingelse.


  What level of dB is the most dominant?


"Dominant" is not defined. Is it "average", is it "median", is it "most frequent value"? All three will give different answers. None of the answers will be relevant at all, again, because of the insufficient sampling. 


  What is the level of background/underlying noise and what is the level of actual sound? 


Impossible to say without a noise and signal model. What's "actual sound" and how does that distinction even matter to regulations?

Generally, hard to tell from a power measurement: You'd have to make assumptions about noise being constant or changing slowly, and I don't see that being true in reality.


  How can I convert dB to dBA?


not at all, per se. dB says nothing about what it was measured to, relatively. Especially, it doesn't say that whatever the volume measurement was based on did A-weighting. So, you only get dB relative to whatever the instrument was considering 0 dB. That being a measurement device, it'll certainly be calibrated, but you'll need to read the manual. Also, the wikipedia article on "decibel" and "dBA", in that order.