Learn Turkish: Keşke o dükkânı açsaymış da kendi işinin patronu olsaymış. - I hear she wishes she had opened that shop and become the boss of her own business.

Both endings express an unfulfilled past wish (usually triggered by keşke). If we used açsaydı, it would mean the speaker directly knows about the situation and is stating the regret. By attaching the inferential -mış to make açsaymış, the speaker is reporting a regret they heard about from someone else: "I hear/Apparently she wishes she had opened..."

If keşke means "if only/I wish", how do we know it's her wish and not the speaker's?

The verbs açsaymış and olsaymış don't have a personal suffix like -ım (first person) or -sın (second person) at the end, which means they conjugate for the third person ("he/she/it"). Because the sentence uses the reported past -mış, we know the speaker is passing along someone else's feelings.

Why is da used to connect the two wishes instead of ve?

In Turkish, da / de is frequently preferred over ve when connecting two verbs, especially when the second action is a natural consequence of the first. Here, becoming the boss (patronu olsaymış) is the direct intended result of opening the shop (açsaymış). It acts similarly to "and so" or "and then".

Can you break down the grammar in kendi işinin patronu?