Sometimes people just kind of modificate the pronunciation of certain words. Listen to yourself speaking your own language & you will notice small fluctuations in various sounds. It's natural & not to be worried about.
If Hieraŭ was supposed to be pronounced with the German or Scottish H it would be spelled, Ĥieraŭ.
You're absolutely right on both counts. But you'll agree that this variety has to remain within bounds. Otherwise, a speaker becomes hard to understand, especially for listeners with a different linguistic background. This is true in any language, probably including Esperanto.
I agree that natural sound drift will always occur, especially with people from diverse language backgrounds. However, the speaker should always make sure that the drift does not overlap too much with other "normal" sounds of other letters. If the overlap is too much, you are simply making the wrong sound at the end of the day (and consequently referring to another letter). Care should be taken, especially in a language like Esperanto where you have close sound pairs: e.g. s and sx, jx and gx, h and hx, etc.
In this case here the speaker is really pushing it in my opinion. He makes a sound somewhere between hx and h, but much closer to hx than to h. Since the word is hieraux and NOT hxieraux, I think this one deserves a rerecording to get it right.
I'm pretty sure it sort of has to do with anatomy of the mouth. If you try to pronounce an h with your mouth in a very articulated [i] position (English: "ee"), the distance between your tongue and your palate (the roof of your mouth) becomes so small that just by exhaling it creates turbulence, resulting in the consonant of the German "ich".
Or in layman's terms: it just naturally occurs for some speakers based on how high they hold their tongue when they pronounce the i. I'd say don't worry about it.
Also, this is actually a different sound from the ĥ (the voiceless velar fricative), which is pronounced with the back of the tongue at the soft palate, while the "ich" sound (the voiceless palatal fricative) is pronounced with the middle of the tongue at the hard palate.
Ĉu essentially means "whether" so: Mi ne scias ĉu ŝi trovis ĝin is a perfectly reasonable statement. What you may try doing is asking yourself if the translation makes sense. Hieraŭ ĉu vi trovis… would actually translate into: yesterday whether you found… or yesterday, did you find… which are actually a bit clumsy.
Vi trovis vian katon hieraŭ, ĉu? however …