Understanding「さえ」and「いてくれる」in「お前が生きてさえいてくれたら」


I'm watching an episode with subtitle that goes:

「俺 ずっと お前が生きてさえいてくれたら と思ってた」

"I always thought, as long as you live on, (I'm ok)"

I have three questions if the translation was correct.

  * Is the "live on / stay alive" meaning provided by (生きて)いる? If yes what does くれる add to this scene, "stay alive for me"?
  * Why is さえ in the middle between 生きる and いる?
  * Can さえ go with たら? Textbook says it always goes with ば




In order:

  * The pure "live on/stay alive" meaning comes from 生きている. The specific nuance of くれる depends on context, but it implies that living on is favourable in some way from the point of view of the speaker.
  * さえ emphasizes 生きる, so that's what it attaches to.
  * Don't believe everything textbooks say. They often simplify things to focus on a specific point. さえ can go with lots of things.

See here for more on [さえ](https://www.weblio.jp/content/%E3%81%95%E3%81%88).

