How is it possible for the MIG 21 to have full rudder to the left, but the nose wheel move freely to the right and then straight or to the left?
Davidw mentioned the book &quot;Red Eagles&quot;.  It has a passage about steering the MiG-17 and says the MiG-21 used exactly the same system.  In the following passage, he is quoting pilot Jose Oberle.
Red Eagles: America's Secret MiGs, Steve Davies, 2011

Taxiing the airplanes was a bit of a trick.  If you wanted to turn
right, you pushed the left [sic][a] rudder bar in and you pulsed this lever on
the control stick.  That dumped the pneumatic pressure to the brake
on the left wheel and transferred it to the right wheel.   You would
get the free-swinging nose wheel to start to turn to the right, and
then as you got ready to come out of that turn you'd have to push the
left rudder bar past neutral and you'd have to start pumping the
little paddle again to get the power back on the left wheel, to get
the nose to straighten out so you could taxi straight!

Per this, the nosewheel is not part of the steering system.
a: most definitely a typo, see for instance the following pilot's experience.
I Was Lucky: I Got to Be a Pilot, Paul &quot;PK&quot; Kimminau, 2017, p. 161

After checking the systems out, I taxied to the runway. That was an
experience in itself!! On US aircraft, the brakes are on the rudder
pedals, that is, you push on the tops which would rotate forward and
apply braking. Also on US aircraft, if you wanted to turn, you pushed
the rudder pedal just as if you were using rudder to fly the aircraft
and power steering would turn the nose wheel. On the MiG-17, the
braking was done with a lever on the control stick. You squeezed it
and applied brakes. If you wanted to turn, you pushed the rudder pedal
in and squeezed the brake lever, and it would apply braking to that
wheel so you turned in that direction.