Hi nikita.
1 - I think you can't hide the others countries, I don't see Google examples with only one country. I think you can fix borders for map, but I don't check this.
But! If you create you own map, ie - get country image and create your map tiles, you can create your own map type and use in component. You can check this case - on Demo Site - NZ Topomaps
2 - If I understand you right - can be placemark as link...
Yes, you can see value for placemark field "Action by Click", there is open link
See
demo
On top left of map. Green fishing icon opens link. (You set Site link URL on placemark and set "Action by Click")
Clusterer works for all placemarks
3 - You can:
3.1 - create placemark groups, set it for placemarks and use feature: placemark management by groups, but it only in component
3.2.1 - create placemark groups, set it for placemarks and call from plugin (in article) by placemark group id
3.2.2 - create categories (in categories tab), set it for placemarks and call from plung by category id
Ie 3.2 - you can create your own list (or menu and etc) with opening for example definite article, and in this article you can call plugin for definite category or group
4 - Yandex Maps - it is Russian JavaScript API Map (it needs API KEY like GoogleMaps v2)
Maps
API