Mi potete aiutare a correggere questi frasi? 

I miei corsi <font style="background-color: yellow;">di</font> italian<font style="background-color: yellow;">o (here the italian language, l'italiano,  is the subjet that you were learning, so it's singular)</font> durava<font style="background-color: yellow;">no ("i corsi" is plural..)</font> sette mesi. <font style="background-color: yellow;">D</font>opo di che, ho partecipato <font style="background-color: yellow;">a </font>dicembre <font style="background-color: yellow;">dell'</font>anno scorso (a cosa hai partecipato? here I think it lacks the object of the verb...), <strike>che peccato</strike><font style="background-color: yellow;">purtroppo</font>, il voto di ascolto non ha superato <strike>la linea </strike><font style="background-color: yellow;">il punteggio richiesto(when we're talking about results, usually it's better  to use the word "punteggio richiesto"= required score)</font>, manca<font style="background-color: yellow;">va</font><font style="background-color: yellow;"><font style="background-color: yellow;">n</font>o(here you're still speaking about something that happend in the pas) </font> solo due voti..Dopo quella volta, ho deciso di iniziare a migliorare il <font style="background-color: yellow;">mio </font>livello di italiano, soprattutto <font style="background-color: yellow;">l'</font> ascolto e <font style="background-color: yellow;">il</font> parlato<font style="background-color: yellow;">.(I'd suggest you to interrup you sentence here, in this way it'll be clearer to understand and also it'd have a better rithm)</font> <font style="background-color: rgb(255, 255, 0);">D</font>urante questi parecchi mesi<font style="background-color: yellow;">,</font>  attraverso* <strike>ascoltare </strike><font style="background-color: yellow;">l'ascolto d</font>i dialoghi e<strike> vedere</strike> <font style="background-color: yellow;">la visione di </font> serie italian<font style="background-color: yellow;">e(if you're not specific about any serie in particolar I'd suggest you to use the plural form)</font>, penso di aver fatto <strike>troppi</strike><font style="background-color: yellow;">molti (troopi means "too much")</font> progressi <font style="background-color: yellow;">in</font> questi due aspetti. Mi pare di riuscire** a<font style="background-color: yellow;">d</font><font style="background-color: yellow;">( we have to put the d here because there is the same vowel two times) </font> addattarmi rapidamente a vivere in Italia.

* if you want to use the word "attraverso" then, you should use a noun istead of the verbs "ascoltare" and "vedere". Attraverso... cosa? attraverso l'ascolto (the listening) e la visione (the act of seeing or watching) di serie italiane, ecc ecc. Hope it'll make sense to you. :) **Mi pare di riuscire is not incorrect but, when you talk about an hypothesis or an idea, it is better to use the conditional tense. So I'd suggest you to write it like that: " Penso che riuscirei...". 

I'm not a teacher and actually I don't remeber so many grammar rules anymore... XP these corrections are just the things that I'd have written....I hope you'll find them usefull.