up/down the street

  1. He lives just up the street.
  2. He lives just down the street.
    What is the difference in meaning between the two sentences?
  3. The police shooting stirs up great unrest among the people.
  4. The police shooting sets off great unrest among the people.
    Are these sentences fine? Do they mean the same?
  5. Are the kids still up and not go to bed?
    Is this sentence OK?
    Thanks.

1/2 the direction.

3/e have similar meanings but are not identical.
stirs up - creates
sets off - begins

  1. Are the children still up and not gone to bed?
    More naturally:
    Are the children still up? Haven’t they gone to bed?

Beeesneees,
1/2 the direction:
What direction ‘up’ usually indicates?
Thanks.

“What direction does up usually indicate?”

Either
uphill (even if it is only a slight slope)
or
from a point which is considered central for that local community
or, in the case of greater distances,
according to the position of North and South.

You could have used the Google ‘forum search’ button at the top of every forum page and found these and more:
english-test.net/forum/ftopic19489.html
english-test.net/forum/ftopic24180.html
english-test.net/forum/ftopic20512.html
english-test.net/forum/ftopic80046.html
english-test.net/forum/ftopic121297.html

Beeesneees,

  1. Change down from fourth (gear) into third.
  2. Change up from second (gear) into third.
    Are they correct?
    Thanks.

Yes, tough you will hear ‘to’ rather than ‘into’.
However, your sentences are not related to the original question. When changing gears there is a very definite direction.