You can build a base on anyone's planet. No restrictions. Most people will probably not even know you built one on their planet. A lot of times it is convenient to do so, so that you can cash in your minerals.
Les Bird
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They're not really secret. They are stars with numbers that have a meaning, for example if you're a fan of Hitchhiker's Guide to the Galaxy then star #00042 will mean something to you. The first one to find a secret star owns it and gets credit for finding it. There are a total of 100 secret stars in the universe.
Sounds like you found a planet with an anomaly. You get full credit for the SETI signal once you scan a planet that has the signal source but an anomaly is a physical object on the planet surface (not necessarily a SETI planet). You have to use your gauges to pinpoint it. One gauge shows how in front of you it is and the other gauge shows you how on top of it you are. It's best to fly and get roughly in the right area and then land and find it.
Tap the CURRENT MISSION button and plot a course to the quadrant/sector. Go to each star system in the sector using your local map and scan the planets until you find it. In your local map you can tap a star and plot a course to it. The local map shows only the stars in that sector so one of those star systems will have a planet that is the source of the signal.