Can I do this with concrete5?
On home and search results page, I would like to make a list of top apartments with short info about price, rating, location. When the user clicks on that apartment he will be taken to a page about that apartment with a full description. Can I make it possible that when my client enters information about an apartment to make specific information visible on each of those 3 pages without the need of typing it 3 times?
It sounds like you are describing using pages and page lists.
Create a page for each property and then add a page list block to a listing page to list those pages.
The basic functionality is very easy in Concrete5, it can get more complex if you start filtering the pages by differeng page attributes but all in all Concrete5 can handle this easily.