Hi, people in Changsha do have accent of the local dialect. But most of them can also speak good manderin. I think it won't be a big problem for your study.
I don't know if the internet in Changsha is so high speed as you think but people in Changsha do surf the internet with the device supported by China Telecom. It is not bad, I think.
To travel between Changsha and Beijing there are many options, you can either take train or flight, they are both very easy.