Not on a horde side, i see flex runs even Normal mode runs frequently advertised on global channel, even alliance has them on occassion.
For battlegrounds? No, realms are connected via cross realm for Bgs (and pve content like dungeons, LFR), there is at least dedicated pvp guild on each side on evermoon.
Although uncommon there are still guilds doing older content, strawberry kisses aussie guild still doing ToT progress as far as i know.
it's 4x xp rate atm and be can be raised further with recruit a friend on website, it's pretty quick if you quest, since dungeons are crossrealm they are tied to tauri realm's xp rate it's usually not worth doing them.