>My question now is, how does these capacitors work?
They act as an extra reservoir for fast current spikes and they short
circuit the large inductance of the supply voltage wiring. By this,
large loops are avoided.
>Sometimes an additional resistor is connected in parallel.
Not in parallel, but in series. This forms an RC-filter, which is way
more effective than a simple cap, correct dimensioning provided.
>What can be the reason that the voltage at the input of the uC gets
>noisy and unsmooth?
It's the micro itself that creates lots of noise on the supply line, by
the internal switchings!
>And why do we never connect the uC directly to the supply but we always
>use a voltage regulator between them?
In battery powered applications this often done. If, on the other hand,
a regulator is used then usually to prevent the micro from being
destroyed by a too high supply voltage.