Elizabeth Phrase in her book "English without tears" explains the difference between a little and little, saying they could even mean opposite things. She gives the following example:
The medicine he took did him a little good.
She explains that this means that the person actually had an improvement as a result of the medicine he took, in contrast to "the medicine he took did him little good" which would mean the medicine actually worsened his condition.
All days and all persons are grammatically correct phrases which mean what they would appear to mean. But there are a couple things to consider.
First be careful when using persons instead of people. People is more commonly used as a plural of person, unless, as onomatomaniak wrote, you want to sound like a lawyer.
Also, "all days" can't really be used the same as "every day" because the former specifes a set of days and the latter specifies that a singular event occurs on each day. So, for example, you can say
I eat an apple every day.
But you can't say
*I eat an apple all days.
If you want to emphasize that every day, without fail, you will eat an apple, with no exceptions ever, you can say
I eat an apple each and every day.
I eat an apple every single day.
I always eat an apple every day.
All of those phrases add some redundancy to "every day" in order to emphasize that you are meant to take "every day" as a literal statement and not a metaphorical statement.
I get stuck in traffic every day. (Well, not on weekends because I don't drive to work on weekends, and not when I'm on vacation, etc)
I brush my teeth every single day (no exceptions).
Best Answer
First variant is OK, the second is almost OK (the apostrophe is absent):
"Two-day" is an adjective here, written as one word.
" two days' " is a possessive form ("an auction of two days").
First variant is more common to use.