Current capacity of very thin (0.1mm ~ 0.5mm) copper wires?
That all depends on the length.

There's two factors to consider with wires:


The self-heating caused by the current
The voltage drop caused by the resistance


Number 1 is purely a factor of the wire diameter.  Number 2 also has to take into account the length of the wire as well.

I find this table is a good reference: http://www.powerstream.com/Wire_Size.htm

0.1mm is roughly 38 AWG.  So for that, for "chassis" wiring (i.e., short runs between boards, switches, lights, etc) the current limit is 130mA.  For longer "power" runs, the limit is a mere 22.8mA.

The resistance of the wire is around 659.6Ω per 1000 feet, so about 0.659Ω per foot.

That kind if wire is usually used for winding your own inductors, transformers, or electromagnets.  It's not often used for chassis wiring without an incredibly good reason.