That's how it's supposed to be pronounced. The German 'y' sounds like a mix between 'ü' and 'i', but it's not used much outside of latin words so I guess it wasn't worth covering on the course. (Not a native speaker, sorry, but I've been going to school in Germany for 6 years.)
It feels awkward because "analyses" is not commonly used. I've never ever heard it used in 44 years and my work involves a lot of analysis. It's always used collectively so the reply would usually be "Yes. Her analysis was good" meaning "Yes. All the analysis that she did over the three articles was good"
In most cases people will think of all the analysis done over the three papers as one thing, so it would still usually be "Yes. Her analysis was good".
This is the same as someone commenting on a colleagues work over many years. You don't say 'His work each day has been good', you just say "His work has been good" which implies his work overall has been good.
The distinction is that "analysis" means both "the conclusion and comments" and also "the analytical skills".
If I want to say that her analytical skills are good, I could say "Her analysis is good".
If I want to say her conclusion and comments are good, I could say "Her analysis is good".
If I want to say that the three separate pieces of work that she drew up separate conclusions and comments for are good, I would say "Her analyses are good". However, if I say "Her analysis is good", I am instead commenting on her skills rather than her reports.
I'm afraid I don't understand how your second example relates. It looks like a different issue.
'Analysis' is singular, and 'analyses' is plural. Your first example means that only one analysis took place. One may be used more frequently, but in some contexts, 'analysis' is wrong.
Analyses is definitely the plural. plural/singular: parentheses/parenthesis, analyses/analysis, bases/basis, crises/crisis, ellipses/ellipsis, hypotheses/hypothesis, theses/thesis. All of these are words from Latin or Greek.
With an American accent, in many places, people pronounce them the same.
Also, people aren't necessarily educated enough to know the singular/plural. Did you know that graffiti is plural and graffito is singular in English? And the plural of cherub in English is cherubim? Alumnus->alumni (and alumna->alumnae)?
Lots of plurals people who are native speakers have never heard of due to a lack of education in that area.
It's also because all those cases inherit the plural rule from their original language, which follows different rules from English. That's why formula is sometimes pluralized as formulae (the original) but increasingly more as formulas (the english version). It's just not fair to expect people to be aware of the original language of the word, and what are the rules fr plurarl in that word. A classic case is octopus. I seem to recall a video in Merriam Webster explaining all the hyper-corrections of this plural based on wrong perceptions of the word being latin or greek in origin.
Count me in with those who used the singular in English here. If someone has analysed three different books, I would still say "your analysis is good", meaning: you analyse well. But if we are talking about a chemical analysis, then it may be more appropriate to use the plural: the analyses (of the various different compounds) are good, meaning that they are all valid or accurate.
It frustrates me sometimes that translations need sometimes to be literal and sometimes to be idiomatic in order to be marked right, and you can never tell in advance.