Learn English – Can we say “I’m going to the bathroom” to mean “I’m going to take a shower / bath”

The choice between down and up for street movement is interesting.

If the street is on a hill the usage is obvious.

If the street is on the level it is less so, but there are some rules of thumb that can be applied.

If the city has an acknowledged "uptown" and "downtown" sections, "up the street" usually goes uptown and "down the street" goes downtown.

Sometimes the choice is made based on compass direction- going North might be considered "going up the street" whereas heading South might be considered "going down the street".

Other times it's local convention- however it got established.

And a lot of times it just doesn't matter and either one is perfectly fine.

But you can get a ticket for public indecency if you are caught "going on the street."!

--get more than a ticket, you would become a sex offender Here's a link to a similar question on English Language and Usage: https://english.stackexchange.com/questions/83597/up-my-street-and-down-the-lane

Your conjecture is invalid.

Follow takes an object and an optional locative complement designating the destination or path of movement. But it never has a causative sense: the subject does not cause the object to move.