Yes, you can only get the same science once, for every combination of situation and biome. The KSP Wiki has a list of these combinations.
This means you can get up to 16 goo readings from the surface of the Mun - since the Mun has 16 biomes, and the goo is biome-specific (not all experiments are), as well as two more in space high and low over the Mun.
Still, returning the same experiment multiple times is beneficial. If you look at the Mystery Goo container, it has a base value of 10 and maximum value of 13. This means returning the experiment the first time will give you 10 science (on Kerbin, where the multiplier is 1), which is 10/13 of the maximum value, or ~77%. Returning the experiment a second time will yield 77% of the remaining three science, so 3 * 0.77 = 2.3 science. Returning it again after that yields 0.77 * 0.7 science and so on. Eventually it won't be desirable to return it again.
Some experiments, like the thermometer, have the same base and max value. this means returning them once yields all the science, and subsequent returns yield zero. The thermometer also has a transmission efficiency of 100%, making it unnecessary to return it at all.
This is for returning the experiment. If you transmit the experiment, returning it still gives you the difference between transmission and recovery.
The goo container has a 30% transmission efficiency, so transmitting it gives you 3 science. If you return a goo container after you transmitted those 30%, you will get 7 science for returning it (for a total of 10), and after that, see above.
Note that you never get more then 30% for the goo container. if you first recovered it for 10 science, and then transmit, you get 0 science, since 10 is more then 3.
As far as stations go, these can serve multiple purposes:
1.) As home/refuel base while a lander travels to each biome, running every experiment, and then returns. The science gets stored in the station, a scientist resets the experiments on he lander, and off it goes to the next biome. after all biomes are done, the science gets transferred to a return vehicle which brings it back to kerbin
2.) The mobile processing lab. This module is often used in the endgame and a centerpiece of a science station. You can bring experiments (even ones you have already returned before) to it and collect data from them, slowly churning out more science while using lots of energy.
3.) Stations are not only used for science. They are often used for refueling. A station in LKO or base on minmus is often desirable to keep the launcher small and then refuel in orbit with fuel mined on moons or from asteroids. in fact, you mostly don't need science stations (there is way more science that can be gathered then that is needed to complete the tech tree, you can finish the tech tree only with science from kerbin, the Mun and minmus) or at most one, while having multiple refueling stations is very desirable.