Not all questions are easy to answer.
Can I use Combine Elixirs with Eternal Elixir to make both parts eternal?
This one is easy: Yes, it works. You still need the highest level Elixir to be 2 levels under half your level, so it's not perfect.
If I'm under the effect of an Eternal Elixir, then retrain out of the feat, do I lose its effects?
You're not supposed to benefit from a feat you've retrained out. So even if the rules are not clear cut about this case, I hardly see a GM allowing you to benefit from Eternal Elixir after having retrained it.
When I use Combine Elixirs to mix mutagen A with another non-mutagen elixir B and then use Persistent Mutagen when imbibing the combination, does the effect of elixir B also persist until my next preparations?
This one is a tough question. Nothing is said of the resulting Elixir when you use Combine Elixir. So you have to expect table variation. I'd personally not count on it, but that's just my opinion.
Thank you!
What is the reason for you thinking that #3 (Persistent Mutagen) is more in question than #1? Is it because it seems comparatively stronger with only a level-2 cap rather than level/2 - 2, and so might go against the "too good to be true" rule? Or are you thinking that the combined elixir might not retain the traits of its parts, like the mutagen trait?
It's because Combine Elixirs specifically states that you create a new Elixir. So it works with Eternal Elixir.
But Combine Elixirs doesn't say how traits are handled. Is the resulting Elixir also a Mutagen or not, we don't know? So you have to expect table variation.