Are there any compact single 18650 flashlights that have output of 2000 lm or more?
The ones I've seen so far don't exceed 1100 lumens
The upcoming ZebraLight SC600w IV Plus is likely the only single-18650 light you can expect to sustain 2000+ lm over a significant amount of time with sufficient cooling. E.g. I'm using my previous-gen SC600 series light as a bike lamp, so sustained high-level output is important for me in this format (but absolutely not at all otherwise). For momentary output there are a few overdriven options such as the aforementioned Emisar D4.
Q1: Are there thermal issues for the 18650 itself or is this just about the emitter getting too hot ?
Normally the emitter itself, but everything can get too hot when high power is involved. Emitter simply has the lowest efficiency in the system because it's where electric energy is being converted into light. At high power levels both the battery and the driver circuitry should be able to retain over 90% (probably closer to 95%) efficiency, whereas an LED can barely reach 20%, with the other 80% of the power fed to it being dissipated as heat.
Q2: If heat dissipation is a size limiting factor, what then is the smallest 18650 light that could "continuously" run eg: a Cree 100 Lumen/Watt light continuously as 1000 Lumen == 10W heat dissipation, flashlight body staying below 50 C at ambient temperature of 25 C ;-) ... Or is that the wrong question and the best trick to dissipate the heat is to keep the flashlight head thermally insulated from the body and give it all the work to dissipate the heat (don't touch the head during operation...).
As mentioned earlier, ZL is known for being able to sustain output without aggressive safety stepdowns in a compact form factor. Also, the trick with heat dissipation is the hotter something is to the touch, the better it actually dissipates the heat. When you feel the light getting hot, what you're actually feeling is the light's body transferring excess heat into your hand. Human body, skin in particular, is an excellent, large surface-area, liquid-cooled heatsink. (Have you ever been to a Finnish sauna or a Russian banya? Funny how well the body works there.) So the firmer your grip on the light, the better it is actually cooled—and, if it's thermally controlled, the brighter it will be. Alternatively, if you're using the light underwater or blow air at it (happens automatically e.g. when cycling), that also works well. Obviously, the light dissipates heat through contact much, much better if the head and the body form one continuous piece of metal—lubed threads are very bad for heat transfer. So you want your compact light unibody if possible, as there won't be enough room for massive fins by definition. If you thermally insulate the head, on the other hand, the body will stay relatively cool, but the head will get much hotter as a result, and will lose brightness.
Q3: If heat dissipation is the issue, would investment into copper help ? Any flashlights with out there ?
And where are you going to put this copper, exactly?.. Naturally, copper is useful as a heat spreader in a MCPCB, but there are still the problems of the interface between the copper and the light's body (typically aluminium; copper isn't as practical by far), and between the light's body and the environment. Those two interfaces are where heat transfer takes the largest hit.
