What is the functional difference between yrke and karriär?
Yrke is your job, karriär is the long-term development of it.
Can I say it using definite form? 'Det är det populära yrket'? I mean do you use 'det är det ...' construction?
Sure! Perfect translation of "It/That is the popular trade."
Why not career?
That would be karriär.
Are 'jobb' and 'yrke' interchangeable?
More or less. Think of jobb as "job" and yrke as "profession".
How do you pronounce yrke?
Ett yrke: https://en.wiktionary.org/wiki/yrke#Pronunciation
Would occupation work as well? It has a broader meaning as it includes unskilled as well as skilled and professional work.
Sure, that's an excellent translation.
Is "work" a good mnemonic for "yrke" (profession)?
Why is wrong "that is"
We do allow that.