Electronic – Did I hook up this CD4052 Analog Multiplexer correctly

The idea behind using a multiplexer is that you would read all of the inputs in a sequence very quickly and then loop around and do it again. It's a trade-off of bandwidth and latency vs. port count. It lets you divide the available bandwidth and required port count down by the same factor. If you have an ADC that can sample at 10 KSps and an 8 port mux, then with 1 input you can sample at 10 KSps on that input, with 2 inputs you can sample at 5 KSps on both inputs, with 4 inputs you can sample at 2.5 KSps on each input, etc. One side-effect is that the samples are interleaved in time as you can't look at all of the inputs at exactly the same time. With 2 inputs, there will be an offset of 1 sample period between readings on alternate channels where the first sample from input 1 will occur at 'T=0', the second sample will come from input 2 and will occur at T=100us, the third sample will come from input 1 and will occur at T=200us, etc.

If you're just trying to read from POTs, you should be fine as the signals coming out of them will change very slowly. All you need to do is write a for loop that will cycle through all of the mux settings and read in the corresponding analog value.

It's likely not possible. The most common failure modes for ICs in my experience are for a pin to fail open-circuit, or short-circuited to either power or ground. For an IC to fail with one I/O pin connected to another one is very unlikely.

To get the behavior you want, you'd have to design an ancillary circuit that detects a failure condition (it would have to detect all possible failure conditions) and activates a second multiplexer to select input from the fail-over input instead of from the first mux. And then you'd have to worry about failure modes of that mux...and so on.