prepositions (examples)?

LatinHello.
I'd like to know which prepositions are possible for each sentence and which ones are definitely wrong. Also what would be the difference in meaning?

Here is what I think:

Shall I buy tickets for/to the concert.
to: more common
for: ok also

The Sahara is one of the most remote parts of/in the world.
of: correct
in: incorrect
Think of it this way: of the many parts in the world, the Sahara is one.

There are two sides to/for/of every story.
to: correct
for/of: incorrect
Just as there are two sides to a coin: heads and tales.

He has gone to live in/to Paris.
in: correct
to: incorrect.
He went to Paris so he can live in Paris.

The dog was picked up off/from the street.
off: correct
from: incorrect
The dog is now off the street instead of being on the street.

She put her hands over/on her eyes.
over: correct
on: incorrect

What can you do to relive boredom on/in a journey.
on: correct
in: incorrect
One embarks on a journey...also okay to say during a journey.

I was with two aunts on/from my mother's side.
from: okay
on: okay...but may be better to say two aunts who are on my mother's side??

The body appeared at/on the bank of the river.
at: correct
on: incorrect
Unless you are talking about on the water at the bank.

They saw an old man with/in a red hat.
with: okay but this implies he is carrying it instead of wearing it on his head
in: this is not possible, unless you are talking about a huge hat

He is a bad influence on/over the other children.
on: correct
over: incorrect

LatinOne more question:

The Sahara is one of the most remote parts of/in the world.
of: correct
in: incorrect
Think of it this way: of the many parts in the world, the Sahara is one.

According to your explanation did you mean of: incorrect in: correct?
Sorry I didn't make it clear with my example..."of the world" is still the correct answer...in retrospect my example is not a good one...please disregard.

They saw an old man with/in a red hat.
with: okay but this implies he is carrying it instead of wearing it on his head
in: this is not possible, unless you are talking about a huge hat

What would be the way to say he is wearing the red hat, with which preposition?
They saw an old man wearing a red hat.

Paco2004Danyoo

I think "an old man in a red hat" is OK. It's just because native speakers say so quite frequently. Am I wrong?

paco

Danyoo

LatinOne more question:

The Sahara is one of the most remote parts of/in the world.
of: correct
in: incorrect
Think of it this way: of the many parts in the world, the Sahara is one.

According to your explanation did you mean of: incorrect in: correct?
Sorry I didn't make it clear with my example..."of the world" is still the correct answer...in retrospect my example is not a good one...please disregard.