The CHALLENGE?

There is no challenge in this project - other than to extract the specifications...

You are complicating this way more than needed, by making premature decisions based on facts that you do not give us - and probably don't have yourself.

No, not just 0..5V inputs. It does not work like that. What kind of sensor, or you will have to spend a huge amount of money on 12 separate conditioning circuits to get the sensors possible to read. No, most sensors do not produce a voltage 0..5V, or allow you to just use a voltage divider. No, no, no. So do specify what sensor! The true voltage range is vital! The output impedance of the sensor is vital! The linearity of the sensor is vital!

School projects fails all the time because people makes assumptions. Is this a school project? It is likely to fail, unless you put up real facts!

And no again. An AND gate will not - I repeat not - be suitable for driving relays. An AND gate is a logic chip to make a logic operation on two or more inputs. It is not a chip to drive relays! The microprocessor will probably have more powerful outputs than the AND gate. And a relay is very special, since it is an inductive load.

Or - wait a minute - you want to save money. So buy very expensive relays with built-in driver electronics that can be controlled from a logic level, i.e. just 0..5V. Too bad they may cost just as much as the rest of the construct (every single one of them).

If you use relays, then you normally drive them with an open-collector or open-drain transistor. Or a special IC with multiple such transistors in the same package.

And if you do want analog sensors, you loose much of your available selection if you require 12+ ADC inputs. It will no longer be a question of a cheap part, but of an available part.

Why do you think a multiplexer is complicated? Because you know that it is complicated or because you assume it is complicated? You are aware that - I have already mentioned it - the multiple ADC inputs on the uC is also multiplexed. You may use automatic chained reading of all inputs, but you often do not. So the program may still perform manual multiplexing, even if the bits are written to an SFR controlling an internal function, instead of an SFR controlling two, three or four external pins of the processor.