Today, many thoughts cross my mind. Today, many thoughts cross my mind.

Here is a more natural alternative: I've been reflecting on inequality today. I would use the phrase "crossed my mind" with regards to a specific thought, not to refer to thinking in general. Eg "It crossed my mind that I should probably phone the GP." "Yes, that had crossed my mind".

Today, many thoughts crossed my mind. Today, many thoughts crossed my mind.

"Many thoughts crossed my mind" doesn't sound very natural. You could say "I realised something today" maybe?

Today, many thoughts cross my mind. Today, many thoughts cross my mind.

or "go through my mind" also, if you mean "today" like "nowadays" or "most of the time" then cool, but if you mean like one specific day, today, then you might need to use past tense.

I started my day in a meeting organized by an organization called “rRethinking eEconomics” and everything was in English. I started my day in a meeting organized by an organization called “Rethinking Economics” and everything was in English.

Proper nouns

I started my day in a meeting organized by an organization called “rRethinking eEconomics”," and everything was in English. I started my day in a meeting organized by an organization called “Rethinking Economics," and everything was in English.

the comma separates the two independent clauses you could think of it as paired up with "and" when there are two independent clauses combined

I felt bad afterward because I spoke with a very strong accent, and I didn’t say much. I felt bad afterward because I spoke with a very strong accent and I didn’t say much.

In the evening, I read some pages of a textbook ofn microeconomics and I found something interesting. In the evening, I read some pages of a textbook on microeconomics and I found something interesting.

Or "a microeconomics textbook". You could also say "came across something interesting".

In the evening, I read some pages of a textbook of microeconomics textbook and I found something interesting. In the evening, I read some pages of a microeconomics textbook and I found something interesting.

In the evening, I read some pages of a textbook of microeconomics textbook and I found something interesting. In the evening, I read some pages of a microeconomics textbook and I found something interesting.

more natural this way

In the chapter I was reading, the author explained somthe basic concepts aboutof supply and demand. In the chapter I was reading, the author explained the basic concepts of supply and demand.

He wrote about the conditions that could cause a displacement in the curve of demand and supply. He wrote about the conditions that could cause a displacement in the curve of demand and supply.

He later proceeded later with an example that was very controversial, at least in my opinion. He later proceeded with an example that was very controversial, at least in my opinion.

He later proceeded later with an example that was very controversial, at least in my opinion. He later proceeded with an example that was very controversial, at least in my opinion.

"proceeded later" is OK, but it sounds a little strange to me, while "later proceeded" is more what I would expect to see or "Later, he proceeded to..."

While on the other hand, althoughIn contrast, demand for professionals' skills increased sharply but the number of professionals only increased gradually, the demand for their skills was higher . In contrast, demand for professionals' skills increased sharply but the number of professionals only increased gradually.

It's not natural to start a sentence with "while on the other hand". It would be a connector within a sentence.

While oOn the other hand, although the number of professionals increased gradually, the demand for their skills was higher . On the other hand, although the number of professionals increased gradually, the demand for their skills was higher .

"while" is unnecessary here, but you could modify these two sentences so it says He described that this is the result of a high supply of unskilled workers but a low demand for their job, while on the other hand, although the number of professionals increased gradually, the demand for their skills was higher. I would personally opt for this longer version.

In search of a different approach, I found that some economists believe that the market is not neutral and it is defined by the people who control it. In search of a different approach, I found that some economists believe that the market is not neutral and is defined by the people who control it.

or perhaps is not neutral, but is rather/instead defined by ...