>1. Halogen vs LED vs Xenon
LED. A Cree MC-E or SSC P7 driven at roughly half power (1.4 amps) would give you the brightness you require. You'd get a floodier beam with a SSC P7, which I imagine is what you'd want in a helmet light.
>2. Light housing
You could adapt an existing helmet light.
>3. Wiring Connectors
1.4 amps are safe for ordinary connectors, you don't need high-current special ones.
>4. Batteries (Lith Ion vS NiMH) It is worth making your own?
I'd go with LiIon: a self-built 2x18650 pack in parallel. Otherwise a single D-size LiIon would do, and would not require you to solder to the cells, but would be bulkier.
>How many volts are needed?
This depends on the driver you're using.
Personally, I'd go for one of
these, since they don't have useless modes and are inductor-free so more resistant to shock; you need to add an AMC chip in parallel to the existing ones to bring the max output to 1400mA (from the original 1050). That driver requires a single LiIon cell, or a parallel-configuration pack.
>Can a light and battery be put together for less than $100? Or am I crazy thinking it could.
It is possible for the electronic side, but I don't know if you already have access to a light helmet/shoulder strap lamp you could modify. You could just get a junked helmet with a broken light, discard the guts and build your LED light in that...
The price of the electronics would be:
SSC P7 or
Cree MC-E: US$20 - US$ 23
Reflector+heatsink combo for
SSC or
Cree: US$ 6.50
Two
driver boards (one to use in the light, one to harvest a AMC7135 chip from): US$ 6.58
2-pack of 18650 cells: US$ 9
Alternatively,
D-size LiIon: US$ 19
Switch: less than one US$
Wiring: price negligible
Heatsink goop: price negligible (do remember to use it though, it's important)
You shouldn't need protected LiIon cells because the driver stops working at 2.6 volts; a LiIon that gets to 2.6V under load will go back to safe voltage once the load is removed. However, if you want additional safety you could get
these (US$ 10) or
this (US$ 22) instead.
Also note that you'll need to add the price of a LiIon charger if you don't already have one.
If, for some reason, you don't want to use LiIon cells, you could build a decent pack with six NiMH AAs in a 3-series 2-parallel configuration. Or just use three C- or D-size NiMH in series. The price for that would differ greatly depending on which cells you chose, which brand and which capacity.
This would get you a dual-mode, impact-resistant light with a runtime of 2-3 hours and an output of about 400 lumens.
On a side note, the board from which you harvest the AMC chip will still work (provided you haven't munged it up during the operation), albeit at reduced power, so you could use it in another project.
Final note: I went with cheap parts because you specifically said you wanted to spend less than $100. If you had more money, you could get AW cells, which are generally regarded as the best there is (the price reflects this, though). Do note that Trustfire 18650s have been tested by CPF members and found out to perform quite well. The D LiIon from DX was tested as well, but I can't remember what the outcome was.
This should be all...