Learn Farsi: ای کاش شادی مردم را می‌دیدم. - I wish I saw the happiness of the people.

It is an abstract noun created by taking the adjective shâd (happy) and adding the suffix -i. This is a very common way to turn adjectives into nouns in Farsi, similar to adding the suffix -ness in English (happy becomes happiness).

How is the connection between shâdi and mardom pronounced?

They are connected by an invisible ezafe (meaning 'of'), pronounced as shâdi-ye mardom (the happiness of the people). Because shâdi ends in the vowel sound -i, the ezafe adds a 'y' sound as a bridge, though it is not written as a separate letter here.

Why is the direct object marker râ placed after mardom instead of right after shâdi?

The word râ must go at the very end of the entire direct object phrase. Because the specific thing being seen is the whole phrase 'the happiness of the people' (shâdi-ye mardom), râ waits to attach to the final word of that noun group.

Why is the verb mididam in the past continuous tense if this is a present wish?

When you use ey kâsh (I wish / if only) to express a wish about a present or general situation that isn't actually happening, Farsi uses the past continuous tense (mi- + past stem + ending). English does something very similar by using the past tense for present wishes, like saying 'I wish I saw' instead of 'I wish I see'.