Learn Turkish: Eksperlerden hangisi bu yeşilimtırak heykeli inceleyecek? - Which of the appraisers will examine this greenish statue?

It means 'greenish' or 'approaching green'. The root is yeşil (green). We add the approximation suffix -mtırak, but since yeşil ends in a consonant, it takes the high vowel buffer -i- to become -imtırak. This suffix is mostly used with colors and tastes (like acımtırak, bitterish).

Why is it eksperlerden hangisi (ablative) and not eksperlerin hangisi (genitive)?

Both are grammatically correct and mean 'which of the appraisers'. Using the ablative case (-den / -dan) with words like hangisi (which of them) or biri (one of them) is a very common alternative to the genitive in Turkish to express 'from among the group'.

Why does heykel have an -i at the end here?

It takes the definite accusative case suffix -i because it is the specific direct object of the verb inceleyecek. The presence of the demonstrative adjective bu (this) makes the statue specific, so the accusative case is mandatory even with the adjective yeşilimtırak in the middle.

Is eksper the exact same as the English word 'expert'?

It is a loanword from French 'expert', so it is closely related. However, in Turkish, eksper specifically refers to a professional appraiser, assessor, or evaluator (such as an art appraiser or an insurance adjuster), rather than just anyone who is knowledgeable about a general topic.