<p>Could you use a 3D printer to make a 3D printer's parts? What is the most of a 3D printer that can be made this way? Could parts that break be replaced this way?</p>

Yes, you can print most of the parts (electronics, linear guide rails, ball bearings and nuts and bolts, etc cannot be printed). Actually this was exactly the purpose of
RepRap.org
:
RepRap is humanity's first general-purpose self-replicating
  manufacturing machine.
and:
Since many parts of RepRap are made from plastic and RepRap prints
  those parts, RepRap self-replicates by making a kit of itself - a kit
  that anyone can assemble given time and materials.
There have been attempts in the past to even replicate the frames of printers (e.g.
Dollo 3D
or
Snappy
, but such designs are not very successful, printed frames are more flexible than metal frames.
I have built 2 custom printers myself using other printers to print parts and printed all printer parts for several others. It is possible to print
your own linear bearings from POM
, I prefer these over the noisy metal bearings.