One of my Blasts shuts off randomly while riding, until I flip the kill switch on the right bar off and on again. I know others have had a similar issue with that switch. My first thought is to open up your kill switch and spray it down with some contact cleaner, it fixed others' issues.
As for #2- The replacement ECM may have some weird tune on it. Seeing as your bike is an '03, you can access the ECM with the free version of ECMSpy and get it sorted out quickly. However, since you can't correctly zero your TPS due to a faulty throttle cable, that would definitely be the place to start.