I didnt' read the whole thread, but I concur with the rec to find a used, rigid-fork mtb off CL. Post links here, you'll get feedback on whether it looks like junk or something reliable. I think you should be able to find something very sturdy and ridable for $100-$150, saving you some budget for new smoother tires (better for pavement than knobbies) and a bike shop tuneup (since it seems you are not up for doing your own maintenance).

As for lights, your bike budget will go further if you spend less. One common recommendation is this, I've gotten one and I don't like it so much, I find the beam pattern way too tight, even with the $5 beam-spreader lens you can buy separately for it. I would instead recommend this regular flashlight. As powerful as a car headlamp, it comes with a charger and a pair of crap batteries you should expect to replace after a few months ($10-15 from an US-BASED online battery store). Attach it to your handlebars with two interlocked hose clamps, crank it down tight with a socket wrench and it'll never move. Aim it downwards so the center of the beam lands about 20-30 feet in front of you, and you will be able to slide the "zoom" to get a wide enough beam to see everything you need, in pitch black.