What is the difference between 'і' and 'и' in a word?
The #1 problem i am having with Ukrainian is memorizing vocab and remembering which one to use for the 'i' sound. e.g Привіт.
Is there any explanation for the reason 'и' is used instead of 'і' and any way to differentiate them? or are the words simply 'just like that'?
The word for 'third' i believe is третій, whereas 'fourth' is четвертий. Why does 3rd have an 'i' where 4th instead has 'и'?
и and і are two different sounds. They sound almost exactly like English i in fit and ee in feet respectively.
The other main difference is that і palatalises the consonant before it (makes it soft, like the soft sign ь does), and и doesn't. Therefore, in declension forms, you can see some words getting endings with а/у/и/е/о, and other words getting endings with я/ю/і/ї/є/ьо.
The -і ending in locative and dative singular of nouns and in nominative plural of adjectives are exceptions, since in most words the consonant must become palatalised there.
Your question is very general, so I will only mention your examples.
"Привіт" is "simply just like that." There are more words that start with "при-" in Ukrainian than those that start with "прі-". My spell-checker word-list has 2111 words with "при-" and only 21 with "прі-".
I would call "третій" an exception, because all other ordinal numbers have "-ий", e.g., десятий, п'ятнадцятий, тридцятий, сорок другий...