Check for codes. If a car runs bad, it should not be driven or even allowed to run. Period. The only exception to that does not apply to anyone asking questions here, and requires training and $5,000 of diagnostic equipment in the car with you. If you don't have or won't buy a code reader, have it towed to a shop or you will damage the engine. If it's easier, remove the ignition module and have it tested at an auto parts store. It sounds like that could be the problem.
The oil and charging lights will come on any time the engine dies because the oil pump and alternator both stop turning.
10,000 miles is way too much, no matter how "good" the oil is. Before I installed a supercharger on mine, I changed the oil with full synthetic every 5k miles, now I change it every 3k. Both of those include 12oz of a high quality additive package, not cleaners and such, but the additives that the oil companies already add to make the base oil last longer. Change the oil while you're thinking about it, and from now on, change it as soon as it turns a light almost rusty color. That may be 2k miles for a while, until the clean oil cleans the engine out. I had to change mine every 2k for the first couple changes after I bought it, but I was able to go to 5k after it was cleaned out. Don't add cleaners to speed up the cleaning either, they are terrible for the bearings. There is no engine that runs clean enough to change the oil at 10k miles.