Transmission problems

Most of what you described has nothing to do with the transmission. Based on the dimming lights, I'd suspect the charging system first, but the lights will also dim when the engine stalls for other reasons. If this is a charging problem, you'll have to catch it while it's acting up to have the tests be of value. Intermittent problems are most often due to worn brushes, but on most vehicles it's much easier to just replace the entire generator.

The diagnostic fault codes should be read and recorded too. If the engine is stalling intermittently due to a failing sensor, there will usually be a fault code related to that if the problem acts up long enough for the Engine Computer to detect it.