1. A lot of Russian families have a dacha.
2. A lot of Russian families have their dacha.
3. A lot of Russian families have dachas.
4. A lot of Russian families have their dachas.
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Which ones are grammatical? Do they have the same meaning?
All are correct, technically speaking, but #2 doesn't make sense. That sentence is implying that many Russian families share one dacha! I don't think that's what you mean.
The others are all fine.
All four sentences are grammatically correct, but they have slightly different meanings.
1. "A lot of Russian families have a dacha."
This sentence suggests that each Russian family has one dacha collectively. In other words, multiple families may share a single dacha.
2. "A lot of Russian families have their dacha."
This sentence implies that each Russian family has its own specific dacha. Each family possesses a dacha individually.
3. "A lot of Russian families have dachas."
This sentence indicates that each family has multiple dachas. It suggests that Russian families collectively own several dachas.
4. "A lot of Russian families have their dachas."
This sentence is similar to the second one in that it suggests each family has its own specific dachas. However, it emphasizes that Russian families collectively possess multiple dachas.
So while the sentences have similar meanings, the choice of articles and word forms (singular "dacha" vs. plural "dachas" and possessive pronoun "their") conveys different nuances regarding the number and ownership of dachas among Russian families.