Nicely written letter. I like the way you chose to keep your sentences short. I am also impressed that you correctly used the words which and that. These are often used incorrectly even by native English speakers. I have some corrections that you might find helpful.

Letter to a Programme (Headings are normally capitalised in a particular way in English)

Dear Sir or Madame,

I'm writing in connection with the comic programme "Politicians in Wonderland" which I saw this morning. 
I must say that I found the journalist very funny and polite.

First of all, he didn't start an argument with the politician that was rude with to him. I totally agree with his opinion about the education with other people. (Grammatically correct but I don't understand what you mean by "the education with other people".)

Then, he did made (or cracked) many jokes. He was very funny.

Finally, he helped a citizen with a problem. He's been very helpful. (This last sentence probably doesn't convey the precise meaning that you intended. It is the repeated use of help that is confusing.)

Your faithfully,

 
Joanne Smith

Letter to a programme

Dear Sir or Madame,

I'm writing in connection with the comic programme "Politicians in Wonderland" which I saw this morning.
I must say that I found the journalist to be very funny and polite.

First of all, he didn't start an argument with the politician who was rude to him. I totally agree with his opinion about the education with other of (other) people.

Then, he did many made a lot of jokes. He was very funny.

Finally, he helped a citizen with a problem. He's been very helpful.

Your faithfully
Joanne Smith