Some may roll their eyes, but I'm answering in the case of chelti, who seem to be the most prolific and destructive miners in the setting right now.
1. I think the difference between a ship and a station is not just construction, but purpose. Any ship can stay stationary and shuttle cargo, and any station should be able to move. Larger chelti mining ships will actually act as a station for ancillary vessels to drag unfortunate asteroids and comets into its grasp, or act as a mothership for exploration or exploitation parties on a planet.
2. Chelti will mine just about anything that's easy to extract or that they need. Mining small planetoids to the core has already gotten them into trouble once during their history. Micro gravity mining is usually done by large motherships that process the ore in space and transfer it onto small freighters which either move it to dedicated factory ships, or load it onto one of the massive, skeleton-crewed barges that travel from the frontier to the homeworld to feed their economy.
Mining on planets is often done using what I've called a "Mobile Platform", think an oil rig with a nuclear submarine stuck through it and giant tracks on the bottom. These are transported to the surface in parts and assembled on the ground, where they spend months digging out mineral deposits or other resources. Strip mines are also popular. The reason I keep tech such as the CFS away from chelti is that the next logical step for them would be planet cracking, ala Deadspace.
Gas giants are mined for their hydrogen, often using long term automated balloon siphons that when full float to the upper atmosphere and are picked up by skimming collection frigates. Other methods include satellites with giant sails in the trails of cythonian gas giants, or nebulae if it's very long-term. When in a hurry, some chelti fleets will use a modified frigate to skim the atmosphere of gas giants to collect fuel, but returns from this are more limited.
3. Currently chelti aren't able to make enough of this stuff to really use it to any widespread degree, and even if they did they consider it an extremely hazardous power source.
4. Chelti tend to keep things running. It wouldn't surprise me if they still had rigs out there running on thirty to forty years old retrofitted with artificial gravity systems and piggy-backed on the FTL of other ships.
5. Sometimes, generally though chelti will usually just give up their cargo to pirates if attacked. Machines and crew are harder to replace than dirt and ore.
6. I imagine a large number of chelti corporations are involved in mining to varying degrees, although from what I've portrayed so far chelti governments also have a heavy hand in mining activity. Either encouraging it or otherwise regulating it.
