I want to run a Joomla site with the ability which users can search between entries (based on beginning and destination cities | Dropdown menus), the numeric amount (from X to Y range | text fields) and some other optional preferences including Geo-map.

Additionally each entry is related to a registered user with a profile, So after searching as public users, They need to login to see full entry details and link to owner's profile, therefore can contact him and so on.

Could I do this with k2? Is there any way to create a form including certain fields that users submit these entries in the front-end of the site?

Thanks in advance

For the advanced search funtionality you will have to develop a custom component.

The other functionality can be done with K2, You simply have to use extrafields and core Joomla! functions for the user/guest check.