Just my opinion, but I'm afraid this is the kind of issue that needs rather a hands on examination. It is not something common, if the CEM is at fault (usually on 04 and 05 years) it will behave differently. May still look at the module with a flash light, search for any traces of water (dried or not). As for the ECU I don't see how it would cause these, normally the ECU (or ECM) also controls the engine. Maybe unlock and pull the steering all the way down and towards the seat, the pop the upper plastic off the steering column, and look inside. The key barrel has sometime issues with the key not turning, a chance the previous owner did some getto fix around it ? I also suggest having the key in POS II when reconnecting the battery, and indeed try not to let the battery fully drain, this may cause some other (annoying) issues. I did use by the past a battery switch like such on the '-' pole
https://www.ebay.com/itm/17mm-Car-Ba...c66377fe22a806