is there any application, that would allow me to display just a certain type of Roads and Points (depending on my choice), say motorways only for example?

You can use the OSMXAPI to download specific data from the database and view this data using the JOSM or Merkaator editor or other applications like Kosmos.

Have a look at each project page in the wiki to find out how to use any of these applications (just type in the name in the search).