What will Sonya's family do this weekend?
1. They will plant potatoes.
2. Her family will plant potatoes.
(Are both grammatical? Which answer is common?)
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1. On weekends what do Sonya and her family do?
2. On weekends what do Sonya and her family members do?
3. On weekends what do Sonya's family do?
4. On weekends what does Sonya's family do?
-They get out of the city and spend time in nature.
(Which questions are grammatical?)
#3 is incorrect. The rest are fine.
Most commonly used are both #1 sentences and #4.
Both options are grammatically correct.
In answer to the first question, "What will Sonya's family do this weekend?" both answer choices are common and grammatically correct.
For the second set of questions, all four options are grammatical:
1. "On weekends what do Sonya and her family do?"
2. "On weekends what do Sonya and her family members do?"
3. "On weekends what do Sonya's family do?"
4. "On weekends what does Sonya's family do?"
These questions all ask about the activities of Sonya and her family on weekends. The difference lies in the usage of pronouns and possessives ("Sonya and her family" vs "Sonya's family") but they all convey the same meaning.