Learn English – Is it acceptable to say “I am off” in meaning that I’m tired or something like that

I don't think there's a specific rule involved here.

It is perfectly fine to use up/down the street/road if the street is flat. Which of the two one would use is more debatable, and somewhat depends on each particular person's point of view.

For example, one way, as you've mentioned, is to chose by house numbering: the way in which the numbers are ascending can be considered "up the street", and the way in which they are descending can be considered "down the street".

Or maybe you can consider the direction in which the street is more... erm... fashionable to be "up", and the other one to go "down".

I would say that in general, if used unrelated to the elevation, these phrases can mean the same, and can be used depending on your own preferences. Also note that "down the street" will always be understood, which I believe is the reason for it's popularity comparing to "up the street".

Off here indicates not the location of living but its source.

The idiom arises in the last half of the 18th century in association with the idiom “get one’s living off (of) the land”, meaning one obtains the income which sustained life by farming or by renting the farmlands one owned to others. Armies were likewise said to “live off the land” or “off the country”—meaning that in wartime they obtained what they needed by appropriating it from the territories they crossed rather than being supplied from home.

A similar use of off appears in the phrase dine off (pheasant, the haunch, six or seven courses) meaning one obtains one’dinner from these sources.

So to say that “She lives off her parents” means she obtains the necessities of life from her parents; to say that “I've been living off rats” means I get my nutrition by eating rats.