Which article should be used?
1 A lot of tourists come to our town during the year/a year.
2 How many days are there in the/a year?
I come across either.
Which article should be used?
1 A lot of tourists come to our town during the year/a year.
2 How many days are there in the/a year?
I come across either.
Just remove it, because it doesn't make sense. "A lot of tourists come to our town" means "They come at a high rate", you don't need to mention "a year" (or per year, etc)
You don't need to say "during the year" because that just means "at any point in time" which is meaningless.
You could say "A lot of tourists come every year", or "A lot of tourists come during the summer" or "in October".
For the second example, you'd probably used "in a year", unless "the year" could be understood from context to be a specific year.
The second example is pure grammar...
Definite article: this year is 2023, so the answer is 365.
Indefinite article: 365, or 366 if it is a leap year.
The first example feels a bit strange, but the same grammar rules apply. I can make it work with either...
Normally we get a few thousand tourists come to our town during a year. Because of the total eclipse, over a hundred thousand came during last year.
NB: I found this very hard to type. My fingers wanted to put "Thousands of visitors a year come to our town." If the visitors are steadily coming, a few a day is thousands per year; but a lot per year has little meaning.