Learn Turkish: Duvardaki tablo orijinal mi? - Is the painting on the wall original?

The suffix -da is the locative case meaning "on" (duvarda = on the wall). Adding -ki turns that location into an adjective. So, while duvarda just tells you where something is, duvardaki means "the one on the wall". Together, duvardaki tablo links them perfectly to mean "the painting on the wall".

Does the '-ki' in 'duvardaki' ever change to follow vowel harmony?

No, the -ki suffix is a famous rule-breaker! Unlike most Turkish suffixes, it almost never changes to match the vowels in the word it attaches to. It will stay -ki after a back vowel like in duvardaki or a front vowel like in evdeki (the one in the house). The only common exceptions are a few time words like dünkü (yesterday's).

Why is the question particle 'mi' and not 'mı'? The last vowel in 'orijinal' is an 'a'.

Orijinal is a loanword (from French) and it ends in a "soft" L sound. Because of this specific pronunciation, it breaks the usual vowel harmony rules and acts as if its final vowel is an "e" or "i". Therefore, it takes the front-vowel particle mi. You might remember a similar exception from A1 with the word saat (clock), which takes saatler instead of saatlar.

Where is the verb in this sentence?