I don't have a regular headlight at the moment because I don't do much riding at night. When I do go out after dark, I use a 4 bean flaslight that mounts to my helmet. It tilts downward so as not to blind drivers but allows me to see and be seen pretty decently. I do have a nice little computer, though. It is a Cateye Velo .5. Nothing really fancy but it gives me the basics. When I bought my Cat, many of the computers did not work well on a trike. This one is a corded model with an extra long cord and works really well mounted to my front derailleur post.

Bike computers measure speed and distance by counting tire revolutions. This is done by mounting a small magnet on one of the spokes, and a sensor on the fork. The sensor 'counts' every time the magnet goes by, and sends this information to the computer, which then displays the information to you.

The sensor can send the information to the computer either wirelessly, or through a wire. The problem is, most computers are designed for wedgies (regular bikes) where the front tire is very close to the handlebars. On some recumbents, the front wheel is so far out in front of the handlebars that the wireless won't communicate reliably or the wire won't reach. In that case, you either need an extra long wire (cord), or mount the computer way out front where it's hard to read.

That's why I prefer to use a GPS instead of a computer, I can mount it wherever I want it. Another advantage of the GPS for me is that I can move it from one trike to another without recalibration. Bike computers need you to 'tell' them what size the wheel is in order to do the math correctly. This is not an issue with a GPS.

That would work, but I would not try to create a battery system to run both. What you gain in technology, you will lose in weight gain.

The Garmin 305 I had for a short while would run for 12 hours. I never rode for that long but I did leave it turned on overnight.

I have an old Garmin 12 that I use, it takes AA batteries. It gets around 12 hours with normal AAs, over 20 with Lithium. The motorcycle battery thing would undoubtedly work, but it sounds kind of heavy.