Assume having an LRC-filter, where first comes L, then R and then C. With L connected to a source showing zero impedance, means an idealized regulator output. What means ringing then?
If into C charge is injected, for instance, because the chip connected to C draws suddenly a spike current, then this arrangemant begins to oscillate: Decrease of voltage at C, due to the short spike current drawn, causes more current to flow through L and R, resulting in an overaction with injecting more charge into the capacitor then earlier removed. An oscillating overaction takes place, where periodically energy is moved from L to C, then from C to L, from L to C again, and so forth.
This oscillation can only be damped, if there's some ohmic losses in this arrangement. This can be the equivalent series resistance of C, the "built-in" series resistance of L or the added resistor R. So, R can be mounted in front of L or behind L, but not behind C! The oscillating current through L and C must also pass through R, otherwise it has no effect.



Filtering means, that there's a low impedance to signal ground, which is provided by C, and a high impedance to Vcc. This can be a resistor R, a choke L or a combination of both.
The higher this impedance is, with same C, the better the filtering is. And where R = 10Ohm only offers 10Ohm for all frequencies, a ferrite choke can give you hundreds of Ohm beyond about 1...10MHz.



This depends on the loads to be filtered: If neither of them produces extra noise, then all can be connected to same filter, provided, supply currents are not too high (voltage drop across R!). But in this example, the 12bit ADC MCP3201 can produce some unsane noise, which could interfere the OPamps. Remember, Vcc of MCP3201 also supplies the digital section inside this chip, which can result in some noise on Vcc. So, MCP3201 should see its own filter.



This is a good idea. Nevertheless, don't forget decoupling measures directly next to these loads! At least a decoupling capacitor should be connected. Relays can also profit from a RC filter, by the way...
Take care, that unregulated supply voltage can reliably deliver sufficient voltage to the loads (relays,...)

Kai