Anywhere in sector space in STO, you can use the Transwarp ability to quickly return to Earth Spacedock. 30min cooldown. You can change instances by using the "map options" menu next to your minimap. The option is also available via your area map tab if you pull up the full map. This is very useful for making sure you're in the same instance as your team.
If your team is all in a space instance together and there is an option to beam down somewhere, you will all beam down together. If you are having trouble finding a star system, check the system list in your map. If you don't see it there, it is in a different sector block. Most missions will tell you the sector name where something is, and you can look at the galaxy map to figure out which sector block you need to be in. By the way, you can also buy star trek credits to make your game more interesting, funny and stimulus.
You can edit your keybindings to bind a key to the walk action. This will allow you to walk, rather than run, in ground areas like stations. You can choose not to show your armor when on the ground by right-clicking the armor in your inventory screen once you have it equipped. You will get a menu that will give you the option to show or not to show the armor. Here is star trek online credits service.