When do controls return to neutral?

If I understand correctly, in a real aircraft, it all just
depends on circumstances, and you don't have to know or care about any
"exact" neutral (?).

Essentially, yes. real aircraft controls have the points that they go
when you apply zero force to them. In general, you trim such that
these points of zero force correspond to the aircraft flying straight
and and level at the altitude, speed and power setting of your
choosing.

Understand that most trim settings (especially pitch-wise) only
correspond to one particular speed (and to a lesser excent altitude)
configuration. That is, lets say I trim for 110 knots at 4000 feet,
75% power, and fly hands off for a bit. now - if I pull back on the
yoke, i'll trade some of my airspeed for climb ("zoom climb")... the
further I get off my "target" speed, the greater the yoke is going to
push against my hands... now - the "weird" thing (not really when you
think about the physics, but certainly not intuitive to sim-drivers) is
that if I then decide to release the yoke, the aircraft will
_completely automatically_ return to its trimmed airspeed, and pretty
close to its original altitude.

It actually won't go straight to the trimmed altitude and airspeed,
it'll do a number of oscilations faster and slower than the trimmed
speed until it ends up back to where it was trimmed for. That is why
flying with the trim is generally a bad idea - fly with the yoke, trim
off the preassure = flying precisely.

(also, just so there is no confusion, this has NOTHING to do with an
autopilot, my aircraft doesn't have one - its simply the way the shape
of the airplane is designed to interact with the airflow).

Do you have a marked "zero point" for the trim,

There is a "takeoff point" for the trim system, generally set to
provide good yoke feel for Vy climbout. Once you are climbing however,
trim is completely relative. There's generally no "Move the trim lever
this much to change trim X mph"... That is a fundamentally backwards
way of thinking. Once you are airborne, simply use the yoke to SET the
aircraft off of its currently trimmed configuration, and then use the
trim controls to adjust the trim configuration to the current
configuration- that is really most of flying.

or do you just trim
until it feels right for the circumstances, and then trim again the
next time as required, without worrying about whether the trim is
truly "zero" or not?

Bingo - that's it exactly.

So in a real aircraft, a different trim position also represents a
different yoke position? That seems logical.

I wonder how fly-by-wire aircraft handle this.

There was some discussion on A.net about this - Boeing goes to great
lengths in their FBW systems to keep the 'feel' of traditional
hydrolics, trim and everything. Airbus, on the other hand, just has
the aircraft automatically and always trim for 1-G flight.

I.E, the airbus actually flies more like your flight simulator than my
Piper

I read that a drawback to Cirrus aircraft is that they use springs for
feedback, so it's hard to tell where the control surfaces actually
are.

I haven't read that either way - but I think you over-estimate the
necessity of knowing where your control's "really" are.

Everything in flying is relative, from the moment you take off, you're
changing from one configuration to another - not simply "setting"
configurations- your control inputs are thus always relative.