Learn Farsi: ما کاملاً در مورد فرضیه‌ی شما و این نتیجه‌گیری شک داریم. - We completely doubt your hypothesis and this conclusion.

In English, you 'doubt' something directly. In Farsi, the verb is a compound: shak dâshtan (to have doubt). You cannot 'have doubt something'; you must 'have doubt about' it. This is why we need a complex preposition of relation like dar moured-e to connect the feeling of doubt to the actual hypothesis.

Since there are two things being doubted, do I need to repeat dar moured-e before the conclusion as well?

No, you don't. Because the hypothesis and the conclusion are linked by the conjunction va (and), they function together as a single phrase. The preposition dar moured-e at the start successfully applies to both items in the list.

Why is there an extra 'ye' sound in farziyeh-ye shomâ?

This is the Ezafe connecting the noun to its possessor. Because farziyeh (hypothesis) ends in a silent 'heh' representing a vowel, we cannot just add the standard 'e' Ezafe sound. We must use a 'ye' sound to bridge the gap, which is usually written with the letter 'yeh'.

How is the word natijeh-giri (conclusion) constructed?

It is a very logical compound noun made of two parts. Natijeh means 'result' or 'outcome'. The suffix -giri comes from the root of gereftan (to take or get). Literally, it translates to 'result-taking', which is exactly what drawing a conclusion is.