1998 Honda Accord 98 Accord stalls while driving

Help, I'm in a dangerous car! For the past several months my car has been literally turning off as I'm driving, leaving me to coast to the nearest safe spot. When it's dying, all the warning lights on the dash light up, sometimes flickering with a clicking sound. When that stops, the only light that stays on is the green "key" light, and the hazards work as well. (As I've learned many times). It seems to happen in first, second and third gears, but never in fourth, never at higher speeds. Also, it never happens in the mornings on my way to work. It seems to happen more often the hotter the day is. Some other symptoms that may not be related: when starting from a complete stop, sometimes it hesitates then goes with a "shot" of gas/power. It also revs higher when shifting into second, but not always. Another odd thing, there is a sort of humming, whirring sound that I can hear when the car is off (after driving) that seems to come from the gas tank/trunk area. It goes on then off, almost rythmically, but stops if I open the gas cap. This may have always happened, but I've never noticed it until recently. Two suggestions I've been given: change the electrical ignition switch or the relay switch. Any advice before I start what I fear will be an expensive process?