Learn Farsi: من تازه محتویات مرسوله را چک کرده‌ام. - I have just checked the contents of the parcel.

By itself, chek karde-am means "I have checked". When you add the adverb tâze, it emphasizes that the action happened in the immediate past, translating to "I have just checked" or "I recently checked".

Why is râ placed after marsoole instead of right after the main object mohtaviyât (contents)?

The direct object is the entire noun phrase "the contents of the parcel", which is connected by the hidden Ezafe vowel: mohtaviyât-e marsoole. The definite object marker râ always goes at the very end of the complete noun phrase, not after the first word.

The word mohtaviyât (contents) ends in -ât. Is this a standard Farsi plural?

The -ât suffix is an Arabic plural ending, but it is heavily used in Farsi for formal or technical words. Here, it creates the plural "contents" from the singular word mohtavâ (content).

How is the present perfect tense formed for the compound verb chek kardan in this sentence?

To form the present perfect, you take the past participle of the verb and add the present perfect endings. For chek kardan (to check), the past participle is chek karde. Then, you add the first-person singular ending -am to get chek karde-am (I have checked).