Question about current & Second season of The Flash [spoilers]

I’m mostly caught up with most of the current season (5), but I’m curious about something. I may have missed an important part somewhere along the line (I never saw the last 3 episodes of season 4, for example), but…
[how does Eobard Thawn even exist? I thought he got erased from existence by the suicide of Iris’s fiancee in Season 2?]

Timey-wimey wibbly wobbly.

It never gets explained. I think the ‘time echo’ thing was supposed to explain it, but it doesn’t hold water at this point.

The timeline is just so twisted into knots by Barry and Thawn and Nora and the Legends that expecting logical consequences from time travel is a lost cause.

Well… that’s kinda disappointing, but not surprising. It’s like the old Danny Dunn young adult novels, where he’d invent something new, it’d fail spectacularly and almost kill him, then he’d fix it and never have another problem with it. Every. Single. Time.

These guys come across something new, it’s a horrific stumbling block for them, then they come up with a solution for it and never mention it again. Food packs for Barry, running faster than the speed of sound, needing to hide Harrison Wells’ face because he’s wanted for murder…

There’s an explanation of sorts in Legends of Tomorrow season 2, where Eobard Thawne is one of the Big Bads. It’s explained more clearly at the end of The Flash season 5, but since you haven’t reached that far, I won’t give it away.