I am still trying to figure out how Eobard Thawne is still alive. As seen in season one of The Flash,
Eddie kills himself
to stop Thawne from going back to his time. But how does Eobard Thawne come back?
Eobard Thawne is never really still "alive" after
Eddie kills himself
What we have after season one is a Time remnant. If Eobard is never born, there is no reason for Eddie to kill himself. If Eddie doesn't kill himself, Eobard will be born. It is a paradox. To prevent that, Eobard will continue to exist until the point where Eddie kills himself.