First and foremost, very few words in English are "perfectly" interchangeable.
NOAD says:
still (adv.) up to and including the present or the time mentioned
yet (adv.) up until the present or an unspecified or implied time
I hadn't thought much about this before, but using the word yet suggests a glimpse into the future:
I can't speak English yet – but I won't quit trying until I do.
while using the word still suggests a glimpse the past:
I still can't speak English – even though I've been trying for 10 years!
I'll try this again; the quotes here are in italics, what follows in [brackets] is what I might infer from the speaker's choice of words:
The bus hasn't come yet [but I expect it will come soon].
The bus still hasn't come [I've been waiting such a long time!]
I think you can even combine both words to express exasperation:
We've been potty training Dora for six months now, but she still hasn't got it yet!
That wording indicates it's been a long time, but there's still hope the desired result will happen eventually. Similarly, going back to your original examples, one could say:
I still can't speak English yet!
By the way, this answer hasn't even mentioned the use of these words to mean "even", as in:
We'll have even more snow tomorrow.
We'll have yet more snow tomorrow.
We'll have still more snow tomorrow.
That's another context entirely.
For the sentence you provided, "I would be grateful if you would acknowledge receipt of this letter," you could use "receiving" in place of "receipt of." "Reception," used to mean the act of receiving, has a connotation that's linked with receiving a signal on an electronic device like a phone or a TV which, if used in your context, would sound strange.
Best Answer
Generally, I'd say no.
Let's look at some examples from the dictionary:
Of the four example sentences here, I'd argue that you could only potentially replace wonder with miracle in the second and fourth examples because they are count nouns.
This could be problematic because wonder in this case means more like "amazing", where as miracle could mean more like "the fact that she exists is a miracle".
The subject matter of this option could be problematic, as miracle has a tinge of divine intervention, which could be argued to disagree with the scientific nature of medicine.
The first, and primary, definition of miracle involves the mystical nature of god.
In this example, you could certainly replace miracle with wonder.