- How far between people (groups and cities) do you need to have population to be able to make several flights to and from orbit without getting noticed?
This answer at space exploration shows how far a launch from wallops island can be seen. So if you want the natives to have no indication that you are there you need your launch sites to be about 400km away from them. Since this is far longer than how far the mining can be detected this is the chief limiting factor.
- Is it possible to trick people in to thinking it is something else (like using mythology?)
For the launches, yes. It's highly unlikely that AD 800 people should be able to identify the rising pillars of flame that a rocket launch is with an attempt to go to space. However expect the natives to be curious and expect them to attempt to travel to the apparent launch sites. So if the launches are visible from native setlements you would want to use a hybrid launcher that can perform low level flight for an extended distance before launching into space. This will allow you to mask the actual launch site from the apparent launch site. So to "trick" the natives into having false belief about your launches just don't avoid comunication. They will come up with explanations, and those explanations will almost certainly be wrong.
For the mining operation it depends on the details of what and how you are mining. Strip mining would not be something the natives would have experience with, however they would be able to identify what is going on. Any tailings will also be identifiable as tailings - even from descriptions, allowing identification of mining. The extent that you produce tailings will depend on the purity of your ore.
Finaly the actual mines, I suspect that descriptions of these from a passerby would not be different than natural caverns. A native mining expert might be able to determine that the caverns are non-natural. However if you are avoiding strip mining and tailings you should be able to hide the mine entrances.
If you don't strip mine, and can hide your tailings, the natives would probably have to observe the mining operation directly in order to identify what is going on.
- Any good idea on how to run mining machines and mechanized humans without getting caught?
As long as you are not doing surface mining, and are not close to within direct visual range of native settlements, just close operations down when a native gets close.
WH40K specific EDIT: In the WH40K universe there are some other conserns. The natives are probably human (Otherwise we nuke them from orbit and don't care what they think) meaning we do not look like aliens to them. Also we have matter annihalation technology like the void grenades that can deal with tailings and similar. - Although this might not be economically feasible. Strip mining would still need to be avoided, and operations should still cease when natives happen to wander close. Masking launches as described above might be harder, the hybrid launchers I desribe would be a custom job. - Which would be heretical and likely leave you in far greater trouble than if you just killed everyone in the closest villages. However vessels capable of both air and space flight is available so you just need to be selective in chosing your launchers. Also care must be taken if relying on mythology to explain away the launches. For obvious reasons the natives might have "myths" similar to "our ancestors rode the between the stars on pillars of flame" - if they to the risk of correct identification of what the launches are increases dramatically.