Hi Evgenii,
Thanks for using the Events Calendar. I can help answer your questions.
is it possible to display events within a period of time and place them on the page?
Unfortunately, we do not have a feature to display by a specific time period. It is something that can be done with some customization, but for the most part that is beyond the support we can provide.
You may want to look at the Event Rocket plugin, it is an unofficial plugin maintained by the Events Calender Developers:
Event Rocket
It does have shortcodes that take time periods and explains how to use them in the FAQ section.
Also, if you think that is something you would like as a feature I encourage you to visit our User Voice Page and either upvote an existing request or make a new request there.
http://tribe.uservoice.com/
How this is done on http://wpevents.net/themes/eventful/pro/ ( block “recommended events” ).
I took a look at that site and all the events are using features from that theme, it is not using our plugin at all. So they have their own coding to achieve their look and feel.
Let me know if you have any follow up questions.
Thanks