There is a huge thread of comments on this in the French-from-English language comments. People from different countries failed to agree on the matter.
A "село" is a rural area with no big buildings, where everyone has their own land. Every family in a "село" grows food and probably keeps cattle or chickens or geese or ducks, maybe bees. It is small. I would never call that a town, it is a village. Many people from the US have said "village" sounds like a word from a fairy tale, but then again, there are not so many villages as I imagine them in the US.
In Ukrainian, there are formally three kinds of settlements: село, селище міського типу, місто. "Село" is a village; "місто" is a town or a city; "селище міського типу" (literally, an urban village) is somewhere in the middle - now that I would call a town. To avoid this awkward big phrase, a small town may be called "містечко". Still, even a big settlement is often called "село" if it's mostly agricultural.
You decide if you want to call a settlement of ten farmers "a town", but I wouldn't. I call that a village.
Yes, tons of them.
Basically, Ukraine is an agricultural country.
I live in the capital, but even here it is still popular to have a summer home called "dacha" where people go to grow their own crops.
A lot of people have relatives in villages. I don't have any, but my boyfriend does, and every once in a while we go to the village on weekends to help with the field work.