not designed to be mounted in this manner
fitson handle bars

You could probably rig something but it is not designed to go on a helmet

No, the design assumes you're wrapping it around the bars. I can't see how you could possibly make it hold onto a helmet.

it wraps around the handlebar, all one rubber casing, non adjustable, so its there or nowhere

Probably not as they are best suited to a round pole.

It seems that it is difficult

depends where you mount it on the helmet, the mounting strap only goes horizontal and cant be changed to a vertical config

you could possilby mount it on your helment if you're lucky enough to have the right size/angle vents. There is little adjustment for this light and is primarlily designed to fit on your bars.

Not really. Might be able to make it work but it's not designed for light, it's designed more so people can see you so head mounting it might be pointless.

Well, it depends.
I have a couple on my helmet, fixed through one of the vents at the front. So, depending on your helmet design, you may find that it is helmet-mountable.
If not, it's still a handy thing to pop on your front fork or wherever, so may be worth buying on the off chance.

I'm pretty sure you can replace the battery (but I haven't done so myself)

no, its not true.
the flash can be properly removed and returned to the silicone / rubber fold.

you can replace the batteries fine, just dont rely on it if you ride in the wet

Batteries are simple to replace, Just push out the back... A one minute job.

The exchange of the battery is possible

I've had this light for a few weeks only, so I haven't had to replace the batteries yet. However, the tiny manual that comes with it explicitly describes how to change its batteries, so I'd guess that you can change them.

yes the batteries can be replaced no problem at all

No, not correct. The batteries are easily replaced.

Having just written a review praising the Beetle, I was a bit panicked by seeing your question as I hadn't seen that review. I've just taken the beetle apart and it seems that you can get at the batteries to replace them.

You just pop the batteries out of the back so yes, you can replace them

Can't tell you a diameter, but I have fitted them to the handlebars of my childrens scooters. The bars are probably smaller than any bike bar. The fit isn't too tight, but because the light is so lightweight, it sit nicely on the handlebar down tube.

Variable widths of handebars. The fixing is flexible.

virtually any bars as they are plastic and can be stretched slightly.

Pretty much anything. They're stretchy rubber so they'll go round oversized 31mm bars as well as standard ones. You can even get them round bars with tape on if you need to.

unless you have an extremely large diameter handle bars then this product will fit , the material is rubber and very elastic.

they will fit standard bars up to oversized road bars no problem

It should fit any bike to be honest. I managed to get it onto my bike over the handlebar tape where i have two layers, the rubber also stretches, but will be a tiny bit of a battle to attach when having to stretch it, but trust me. It should fit.

the beetle fits my road bike but it would struggle to fit anything bigger

Pretty much any - stretches round handlebar and hooks back into itself.

The Knogs will fit all sizes from 25.4 to Oversized - they even fit my helmet between the vents as the silicone loop is so stretchy - have even heard of people wrapping them around the headtube! I have the Frog strobes