A man who called
Let me fix you, correct:
- Чоловік з України дзвонив • A man from Ukraine called
- Чоловік дзвонив з України • A man called from Ukraine
Yes, чоловік can only be in the Nominative if it’s the Subject.
But not in all the situation verbs can just change a related word, but prepositions — yes. Need just learn pairs of verbs with prepositions with their cases, also you can see the last paragraph here about a few notes with з. In this case з is a preposition as from and changes the related word into the Genitive case.
And yes, the difference in correct meaning might be understood by word order. But remember:
- Sometimes somebody can play with words' meaning;
- In a real speech, you can understand by pauses or intonation, context.
The girls and freckles
That is why the comma is an important part here, especially in the Vocative case:
- Girls with freckles, unite! • Дівчата з веснянками, обʼєднайтеся!
- Girls unite with freckles! • Дівчата, з веснянками обʼєднайтеся!
In a real speech, again, you can understand by pauses or intonation. Notice that з as with change the related word into the Instrumental case. Or in the second sentence just move the part з веснянками to the end. And just for vocabulary, веснянка has synonym ластовиння.
The big man
Just to notice, in almost all the standard cases, adjectives are written before a noun, just as in English. That is why:
- Великий чоловік • The big man
Here is an adjective for the Subject noun, so in the Nominative case. Of course, you can say the adjective after the noun, but it can be a little strange, poetic, archaic etc. So, but in your sentence:
- The man is big • Чоловік є великим
Big is not a Grammatical modifier (означення) for the Subject but close for (if I did not make a mistake) the Predicate and in the Instrumental case.
And just for comparison:
- Чоловік великого розміру • The man of big size
Here is the Genitive case.
The prepositions з
With the Genitive case:
- A movement from the inside, from a certain environment, from the surface: зі школи • from school, з поля • from the field, з хмари • from the cloud, з роботи • from work;
- A reason, basis of action: з жарту • from a joke, з нудьги • from boredom, з холоду • from cold, з дозволу • with permission;
- A material, implements: з дерева • (by) from a tree, з чашки • from a cup, з лука • with an onion;
- A sign for the branch: (підручник) з географії • (textbook) in geography, (фахівець) з медицини • (specialist) in medicine;
- The object of negative attitude: (глузувати, насміхатися, знущатися, кепкувати, глумитися) з когось • (ridicule, laugh, mock, cheat, mock) from someone.
In conjunction with the Accusative case of the noun, the preposition means "with an approximation, comparison": з десяток • about ten, з годину • about an hour, з діжку • about a barrel, з кулак • like a fist.
In conjunction with the Instrumental case of the noun, the preposition "with" indicates the interconnection of objects, the accompanying circumstances: з братом • with a brother, з людьми • with people, з шумом • with noise, з плугами • with plows, з проханням • with a request.