Hallo Bogdan,

1µA is maximum input current. Along 2k2 resistor voltage drop is 2.2mV. With Vref = Vcc = 5V LSB is 4.88mV. So, your error is less than 1/2LSB. Keeping in mind that typical input current is even much less than 1µA, 2k2 resistor is a very good choice.
Capacitor is calculated by 'formula' tau = R x C. From tau >= 500µsec is follows C = 227nF. So, a normal 220nF capacitor is allright. But do not use poorest ceramic type. X7R should be used or better mylar foil type, like MKS2 from WIMA.

You asked whether it is a problem that C is in parallel with internal sampling capacitor. It's not a problem, at all, but just the clue! Input stray capacitance is Cs = 12pF, it's static, all the time being parallel with C, so not presenting a problem. Actual sampling capacitor Cc is very small: Cc = 2pF. If channel multiplexer is switching-on according channel this capacitance is charged. If your amplifier which drives input of ADC is very slowly, not being able to charge this capacitance in time, then C helps. Assume, that no current is flowing through 2k2 resistor. Then all the current to charge Cc must flow from C. As consequence, while Cc is charged, C is discharged. But because C is so much bigger than Cc, error stays negectable. For 10bit ADC comprising of 1024 steps C should be about 1000times bigger than Cc. So, being Cc = 2pF it results that C should be bigger than 2nF.
After aquisition of input voltage slow amplifier has enough time to fix the discharge of C, so that at the next aquisition of input voltage C is again representing correct voltage.

What does it mean: Slow amplifier?
Data aquisition needs 6T (machine cycles). So, when running mcu at 30MHz amplifier must settle within 2.4µsec to less than 0.1%. If amplifier is slowlier only big C helps. If amplifier is fast enough directly driving input (then without C!) will satisfy.

Up to now, we only discussed RC-filter as being something necessary for improving sample/hold performance of mcu. But it's only well suited for sampling some slowly varying DC-voltage. If there are AC signals with heavy amplitudes and high frequencies we have to do something to prevent ADC from violating Nyquist Shannon theorem. At 30MHz clock frequency of mcu a conversion needs about 20µsec. If we use all 8 channels we can actualize each channel every 160µsec, giving a sampling frequency of about 6.3kHz. On the other hand our RC-filter gives a corner frequency of 1 / 2 / pi / R / C = 330Hz.
If we want to use a signal bandwidth of 330Hz, our sampling frequency must be at least 660Hz. But this will only satisfy, when frequencies >= 660Hz have amplitudes of less than 60dB (1/1024) of maximum level. If they are present with much higher amplitudes RC-filter's dampening is not good enough, only poor 7dB!
Then two ways are possible. Drastically increase of sampling frequency, which can be done up to 6.3kHz/channel or use of additional, much sharper low pass filter.

To your question, whether this RC-filter changes signal: Yes, your signal is low-pass filtered.

Bye,
Kai