Multiple Analog input for one channel ADC with Amplifier drivers?
The right thing to do for any application is to make sure that you buffer the signal sufficiently before you feed it to the ADC.

How much buffering you need depends on the impedance of the source and the impedance of the ADC – which in turn will be given in the ADC's datasheet. Usually, we use ADC buffers (opamps in voltage follower configuration) to drive ADCs.

So, really, make all three inputs buffered. A quad-opamp IC costs literal cents, and the voltage follower configuration is really nothing but the input signal connected to the non-inverting input of the opamp, and the inverting input connected to the opamps output, and use the latter to drive the ADC. So, that's the cost of one connection plus the cost of one quad opamp to give every single input a reliable buffer. Do it!

Switching: You can switch buffered signals using an analog switch, but you shouldn't do that for high-impedance signals, typically. So, voltage buffer for each input, switch after that, ADC last.