A simple text to correct with new words learned wording

When I feel backed into a corner and the everydaylife becomes too tough, I step away from the city, take my car for a spin and pick the first highway to head out.

I pick some songs to listen to, and sometimes I sing aloud, unless someone can see/hear? me.

Sometimes, when I go back home, I find solutions to make things go higher to thrive.

Do you mean,
“…I find solutions to improve the situation.”
“…I find solutions to make things better.”

I may make anysome mistakes, feel free to correct my text at will.

Thank you for reading my text.

“Thank you for reading.” is not grammatically correct. It’s not a sentence. You can say, “Thank you for reading this.”

A simple text to correct with newly learned wordings

Did you mean to say you are using new words, phrases or grammar? We don’t usually use wording in this way, but I changed it to words in this case.
I changed “new” to “newly” because “new” is an adjective, but you need an adverb.
Adjectives are used to describe nouns, and adverbs are used to describe verbs. Adverbs usually in -ly like “newly”.

When I feel backed into a corner and the everydaylife becomes too tough, I step away from the city, take my car for a spin and pick the first highway to head out.

Life sounds a bit more natural than everyday in this sentence.

I pick some songs to listen to, and sometimes I sing aloud, unless someone can see me.

You don’t need a comma here after “aloud” because “unless someone can see me” is a dependent clause.
Independent clause => a phrase that can be used by itself Example: “Sometimes I sing aloud.”
Dependent clause => a phrase that cannot be used by itself. Example: “Unless someone can see me.” does not make sense by itself because we don’t know what people can see you do. What are you doing? So this sentence would need to be attached to an independent clause like “Sometimes I sing aloud”.

When the traffic is moving smoothly, I relax and think of many things without pressure for the time being.

The sentence sounds a bit awkward, I removed “for the time being” because you already said “when the traffic is moving smoothly,” You already described a time when you are able to relax and think, so you don’t need to describe it again.

Sometimes, when I go back home, I find solutions to make things go higher to thrivey problems.

We do add commas after “sometimes” but in this case you do not need it.
I don’t know what you mean “to make things go higher to thrive.” Do you mean you find solutions to make you successful? You could say “I find solutions to my problems.”

I may make any mistakes, so feel free to correct my text at wills needed.

You don’t need to say “any”, since you already said “may” to describe the possibility of making a mistake.

I added “so” to make the sentence sounds smoother.

“Feel free to correct my text at will” sounds correct, but it very formal. (It sounds like historical writing.) You can say either:

“correct my text as needed” => correct mistakes when you see any mistakes.
“correct my text as you wish” => correct mistakes only when you would like to.

Both would be correct and polite, but have slightly different meaning.