Is the accent on the '' И '' in the '' Мій '' word is important? because I wrote without accent and it wrote to me that the answer is correct!
Important is that those are two totally different sounds, in fact, и is a vowel, and so й it is not an accent, but a separate letter. Accents are normally not used in Ukrainian.
Is мій and моя interchangeable or is the first one strictly masculine and the other feminine
There should be another option for 'dad' - 'ватько' (very common in Ukraine).
In Russian, й is often written as и (especially colloquially), even though they are technically different letters. Is Ukrainian similarly flexible?
I am not sure what you are talking about. In Russian "й" is a separate letter and sound, even though there is a blurry line for some "-ие" / "-ия" nouns (e.g., сомнение / сомненье)
You probably mixed it up with "е" and "ё". :) Putting dots over "е" is indeed optional, but it's not the case with "и" and "й".
whats the difference between Miy and Mayo? Is Mayo in regards to female and Miy for males?
There's no mayo in Ukrainian.
There're masculine "мій", feminine "моя" and neuter "мое"