I am thinking of purchasing a few 'American FL's, and what would be the most matching gear for the lamps to run on?
1. PL 13W (GX23 base): I tried to run these on a regular PL-C 13W ballast, and it won't work. A 15W T8 ballast did successfully fire these up.
2. Slimline T8/T12: any electronic IS ballast?
3. HO T8/T12: HID ballast?
4. VHO T8/T12: HID ballast?

There are no PL-S 13W ballasts in Europe.
Slimline T8/T12 requires an instant-start ballast.
HO/VHO T8/T12 requires rapid-start ballast.
You can find export US ballast for 240V 50hz areas, at eBay.
Eltam here, produces a rapidstart ballast for a single F96T12 -HO lamp.

1. PL 13W (GX23 base): I tried to run these on a regular PL-C 13W ballast, and it won't work. A 15W T8 ballast did successfully fire these up.
It is 0.22A lamp (reason is to suffice with just a series choke on 120V), so F15T8 ballast is very close to the rated current.
The PL-S 5..11W and 4..13W T5 are rated around 0.16A, so their ballast will underdrive the US PL13W.


2. Slimline T8/T12: any electronic IS ballast?
Many cheap electronic ballast may operate these lamps (short the heater connections), but the problem is, the ballast will blow within seconds once the lamp fails to strike or become missing.

3. HO T8/T12: HID ballast?
4. VHO T8/T12: HID ballast?
Depends on the arc voltage: Below ~110V just a transformer to feed the filament will suffice (plus a HID ballast with close or slightly below the rated current).
Above ~120V arc the mains voltage of 230V will become too low OCV for a stable and reliable arc, those lamps won't work.

Regarding importing a 240V US ballast: That may work, but only with electronic ballasts. Don't try with magnetic (you do not know, whether they are using inductive or capacitive reactance, you would have to reduce the voltage by 20% which will lead to ignition problems), so magnetic will likely not work...

I would be also suggesting electronic multi-volt US ballast, thats probably most easiest way. I have couple GE proline T12 rapid start ballast that I've been using to run 40W t12 lamps succesfully with 230V 50Hz input. They are rated for 120-277V 50/60Hz.

The US 13W PL : Try 2 of them in series on 18W T8 ballast

I use the same choke for F15T8 and PL-13. If the choke lists one, I may use it for the other if I need to. I can't see why this would not work with a 240V choke for F15T8 lamps, and you seem to have found the answer.

I have some ballasts here that are listed for both the F15T8 and the PL-13.

The US 13W PL : Try 2 of them in series on 18W T8 ballast

That would be too much current - the F18T8 is 0.37A, the PL13W 0.22A...

The 2x13W PL in series have ~130V arc voltage. I am trying to extrapolate from the rated lamps for this ballast :

18W T8 - 60V arc - 370mA
26W PL - 100V arc - 315mA

It looks like its gonna be below 300mA.. Worth a shot