Regarding those contracts about placing a satellite (or something else) around some planet or moon... May I dismiss them after the contract is fulfilled? Or there is some kind of penalty if I do that (like, the company not making new contracts with me again) ?
Once a satellite completes its mission in can be removed from orbit. But this isn't recommended for the following reasons:
- A satellite in stable orbit can be re-contracted for easy money. The new contract involves moving the satellite to a new location.
Example: I launched a satellite to Kerbin equatorial orbit which paid around K50,000. It has since been re-contracted to move to a new orbit twice paying an additional K45,000. I had left enough fuel to de-orbit but each of the contracts only burned 1 unit of fuel!
- In KSP 1.2, satellites can be left in orbit to form a "Deep Space Network" of telecommunications.
Yes, once you've completed the contract, you can do whatever you want with the satellite.
If you have multiple satellite launch contracts active at the same time, you can even complete two (or more!) of them with a single satellite, as long as it's got enough fuel to reach both orbits and the parts required by both contracts. Just get the satellite into one orbit, wait the required 10 seconds for the contract to complete, and then move it into the next orbit.
However, there are several reasons why you generally shouldn't just blow up or de-orbit a perfectly good satellite:
Contracts for "science data from around <planet / moon>" are pretty common, and can be trivially completed if you already have at least one satellite in orbit around the planet / moon with an antenna and at least one science instrument. (Thermometers are a good choice, being cheap, lightweight and reusable.) Note that such contracts don't actually require you to gain any new science points from the data — you just need to collect and transmit it, even if it's worth zero science. For the same reason, it's a good idea to leave working landers on as many planets and moons as you can, since you do get contracts for surface science as well.
Once you have some satellites in orbit, you'll also frequently get contracts to reposition one of them into a new orbit. Usually, the new orbit will be pretty close to the old one (often just a slight plane change), so completing those contracts is pretty easy as long as you have some maneuvering fuel left.
Also, as already noted in other answers, in KSP 1.2 satellites can be used as signal relays, and the more you have, the less likely you are to lose control of your unmanned vessels at a critical moment just because of a gap in your relay network. Do note that, for a satellite to be usable as a relay, it needs to have a relay-capable antenna.
BTW, when "mothballing" a satellite, make sure that its solar panels are facing the sun so that it won't run out of power. Having some fuel left for future orbit changes is also a good idea; if your tanks are dry, and especially if you have other satellites nearby, you may want to consider terminating the satellite just so that you won't get any more contracts to move it later. Of course, you can also always just decline such contracts, or, if you prefer, launch a new mission carrying extra fuel and a klaw to grab your satellite and move it. ;)