Can multiple LC circuits be connected to the same antenna to listen to different frequencies all at once?
Yes, but there will be interaction between the circuits. For example, if you were to directly connect two capacitors of two tuned circuits in parallel, the result would be the sum of the two capacitances. To tune multiple frequencies requires some isolation mechanism, e.g. resistors between each tuned circuit.

It depends on how far apart the frequencies are, as well. For example, two FM broadcast stations just a few hundred MHz could be amplified by a single broadly-tuned front end (RF amplifier) connected to the antenna, mixed with a signal from a local oscillator, and then fed to two intermediate-frequency amplifiers and detectors. The audio output could then be mixed and sent to a single audio amplifier.