Yes, Slovak is very similar to Polish so I guess  a lot of words sound familiar to you. I was in Bratislava last Saturday and I could understand a lot even though I don't speak your language :)

My first day in on Italki (wrong prep)

Today I'am  have started (you need the present perfect tense as 'today' is not finished the moment you mention it) in on (prep) Italki and make made (past simple since you refer to the past; 'make' means it's a habit) a good friend where ('where' refers to a place) and  we talked (past) for on (prep) skype during for some minutes. I want to (infinitive after 'want') learn English because it is (you need a subject) a desire from since my childhood.

P.S. Since + a point in time (in the past), until now.

For + a period of time

Some words i retired of google translate why i not know, I (have) checked some words on google translate because I did not know them. Please correct them for me.

My name is (avoid contractions in writing, plus I'm is mainly used in speech) Saeid Gharaati. I have graduated (present perfect for life achievements) from Azad University of Isfahan. I have a B.Sc and M.Sc in food science and engineering where (relative pronoun where to link two phrases) I defended my thesis in September 2014. I have (no contractions) been teaching in Fadak Technical and Vocational University since 2012. I have also worked with other universities including Iranian Food and Drug Organization in Kashan University of Medical Sciences in order to improve food quality since 2015. Moreover (use linking words), I have participated in meetings of the Iranian National Standards Organization for standardization of food industries and have had (present perfect)about 660 hours of training related to my field of study. That is the reason why I am (so) interested to pursue my studies/finish my PhD degree.