Is there a direct way to download a full coverage, actual (2017), cloudless, mosaic of Sentinel-2 satellite imagery to a whole country (with the size like Portugal) ?
If it isn't possible, then can you advise me recipes to do it?
Creating a mosaic can be quite a complex topic - you have to select each individual pixel based on chosen parameters, either creating a median value, darkest pixel, average, ... Depending on this you will get more or less consistent images, e.g. neighboring pixels might be chosen from separate dates, one showing harvested field and one still growing vegetation.
I suggest you check Sentinel-2 cloudless (https://s2maps.eu/) - here you can download the data for free.
Alternatively you might want to check Sentinel Hub services (http://www.sentinel-hub.com/develop/capabilities/wms) where you can get a pretty decent approximation for cloudless mosaic by e.g. setting "get data from 2017-01-01 to 2017-12-31, priority = least cloud coverage". The benefit here is that you could get up-to-date data as well, if you would need that. (note that Sentinel Hub services are not free).
Disclaimer: I am working at Sinergise, company behind Sentinel Hub services.