ქართულის სირთულები და ჩემი ქართულის მასწავლებელი, ალექსი

*ქართულის მასწავლებელი- It is a possessive form, like "my Georgian teacher", so it has to be in Genitive case.

*შეუძლებელია იქნებოდა- "ა" in the ending, is the short form of the verb "is" (არის). You already have the verb იქნებოდა (would be), in the sentence, so don't need to use two verbs, because translation is like that " there is would be impossible". 

*მეგობრულ კაცს- The sentence has to be in Dative case, so that's why we added "ს" in the ending.

*ქართულის სწავლაში - We say this way, because we want to express, that someone helped me AT learning the Georgian. This is why we add the suffix -ში

*სრულყოფილი არ არის- negative word must be always in front of the verb. 

*გპირდებით- means: I promise someone (third person). It sounds like you promise something to someone directly, and don't say "I promise" in general. When you want to say it in general, it is better to use the form "გპირდებით", or "ვპირდები ჩემს თავს " (I promise to myself) 

Well done! Keep going this way :)