1. Where is today's newspaper, honey?

2. The park is within an hour's walk
from here.

3. The bakery is within five mile's
distance.

3-1.The bakery is five miles' distance.

4. I bougth ten dollars' worth of food
at the supermarket.

(Are they all grammatical?)

#3 The better way to say that is The bakery is five miles away. or The bakery is within five miles.

The rest of them are correct.

1 - OK

2 - OK ("an" indicates a singular, so "hour's" is correct)

3 - Not OK! ("five" indicates plural, so you need miles' - plural possessive)

3-1 is incorrect; you could write The bakery is five miles distant.

4 - correct

1. Where is today's newspaper, honey?

This sentence is grammatically correct. It is asking for the location of the newspaper.

2. The park is within an hour's walk from here.
This sentence is grammatically correct. It is indicating that the park can be reached within an hour by walking from the current location.

3. The bakery is within five mile's distance.
This sentence is not grammatically correct. The correct form would be "The bakery is within a five-mile distance." It is describing the distance to the bakery.

3-1. The bakery is five miles' distance.
This sentence is not grammatically correct. The correct form would be "The bakery is five miles away." It is stating the distance to the bakery.

4. I bought ten dollars' worth of food at the supermarket.
This sentence is grammatically correct. It is indicating the value of the food purchased at the supermarket, which is ten dollars. The use of the possessive form ("dollars'") is appropriate in this context.