LIGO's detection of gravitational waves can help estimate Hubble's constant in a new way. Another paper might be informative. Apart from that what information can we get from the observed gravitational wave?
The paper you list as another paper is the primary paper. You cant measure H, unless there is an optical observation of the event. GW tells the luminosity distance, optical counterpart tells its redshift. Use the two, get your H.
Second part of your question is too general. LIGO has tried to cover a bredth of topic since the first detections and information is listed here, https://www.ligo.caltech.edu/page/detection-companion-papers
If you want a superficial answer before you jump into the papers for a few weeks. Here it is
1) One can test if observatons withold general theory of relativity of violate it. There are many ways to do this but LIGO has tried to follow a model independent approach 2) One can estimate the parameters of the observations and estimate the mass and spin distribution of the sources along with their rate of mergers. 3) One can talk about things like extreme-gravity after looking at signals produced by BNS>
GW astronomy is just beginning and I am sure a lot can be done.