American students also tend to stumble when they encounter the Russian letter Щ (shchah), but are told that they say it effortlessly whenever they say "English church" or "fresh cheese."
You've inadvertently hit upon one of my pet peeves, NorthAmerican.
They are, indeed, often "told" this--it's the explanation used in countless textbooks over the years--but it strikes me as quite wonderfully bogus. When I say "fresh cheese" or "English church" there are, unmistakably, two distinct consonantal sounds /sh/ and /ch/, not the requisite elongated voiceless alveolo-palatal fricative of Щ (IPA =/ɕɕ/) . Even if you do manage to sort of slur it into one word (freshcheese, englishchurch) you're still not producing the modern Щ--the consonant cluster produced thereby (/ɕtɕ/) would be a historical pronunciation, not how щ is said in modern Russian.
Better advice is given to students of Mandarin, which has almost the same sound (represented in pinyin by 'x') but shorter (/ɕ/). Grin tightly and say "sheep" and you'll produce a close approximation of the needed sound. (Delete the 'p' at the end and you'll be saying the Russian word for cabbage soup.)
I'd also say there are other Russian sounds that you neglected to mention that are even more likely to cause English speakers grief: ы and certain softened consonants (especially ль and дь) come to mind. And the English sounds that Russians struggle with include 'th' (i.e. /θ/, /ð/), the 'a' in cat (/æ/), 'j' (/d͡ʒ/), soft 'h,' and any consonant cluster that includes a 'w'.
As for sounds that I, personally, find difficult, the bane of my existence is the Arabic ح (voiced pharyngeal approximant) which I can sometimes get right, but only by accident.