Keeping a standing neutral or, preferably, friendly towards the Libertonian law enforcement will naturally have a good influence on your license application. I wouldn't recommend you do anything other than what you already are. Your attitude towards the law enforcement and in Liberty in general is excellent.
As for the anomalies you showed me, they are used by various research and science vessels in order to obtain scientific data. Using specific scanners you can extract this data out of these anomalies, however there's very few ships in Sirius that have this capability, and not being the captain of such a ship I could not tell you the specifics behind the methods used to extract such information.
As far as I'm aware, however, the anomalies are completely harmless.
Please, do feel free call me by my first name, Maria, as well.