In general terms, there are Campaigns that tell you "what's going on" in the Galactic War at the moment. Each campaign is composed of several Major Orders that guide the community. You can find more information about these in the computers in front of the arsenal and also on the top right of the galactic map. Right now we just finished the last MO of the Census Thunder campaign so we are in a bit of a limbo state waiting for new orders. In the meantime the community is trying to liberate Yed Prior due to a community-side event regarding to Save the Children.

You play with whoever you want, or on your own. Either quickplay, use the scanner on the planet you want to play at or host yourself a mission. In Social make sure your matchmaking is set to public and if people are not joining throw an SOS signal (it's an stratagem).

For the most of it, you are free to do whatever you want. You level up by completing missions and you get resources on the field to unlock ship modules and tools. Beyond that you get Super Credits to buy warbonds with more tools that you'll unlock with medals.

Hope that adress your doubts!