Yes, this is exactly the challenge. It extends far beyond just ad-targeting. On the database side, social network sharding, replication, and caching schemes aren't typically designed based on national origin of users.
If you have a full datacenter (i.e. containing databases, not just a frontend or CDN / PoP footprint) in a country, then typically the entire logical data set -- all data for all users worldwide -- is presumably replicated there. Other systems and services will then make assumptions that any object can be looked up with low sub-ms latency.
Social networks often contain activity streams and other pages that include content from many users at once. Consider algorithmic ranking of feed content, comments on popular page content, etc: how do you even implement this if even some small subset of the data needs to be fetched from halfway around the world on every page view?
Anyway, to answer your original question, friendships are bidirectional associations and would typically be stored in two places: one entry in your db shard, and one entry in your friend's shard. Photos are objects and presumably would be "owned" by a single user or page and located there (at least in terms of the metadata about the photo); however tags may be associations which have entries on multiple shards just like friendships. If some of these shards can only be accessed across a trans-Atlantic link, the entire scheme falls apart due to the latency.