To my knowledge Blizzard has not yet provided a way to view friend status from outside of their games. So you'll have to go with a 3rd party solution.
I use Steam to launch World of Warcraft. Steam will notify my friends when I launch a game, and vice-versa. Most of my friends also use Steam, which increases the value of Steam tremendously. There's little quite as satisfying as launching WoW and then seeing 4 more of your friends follow your lead. One downside to Steam is you have to own at least 1 game on the service to get the friend features.
Also, steam doesn't tell you what character they're on, but once you're in the game RealId can help figure that out really quickly. If you don't use RealId with these friends, there are a number of friend-synching addons you can use to keep track of friends across multiple characters on the same server/faction.
There are also a few alternatives to Steam (XFire?) for keeping track of what your friends are playing. A common thread across all of these is that all your friends will want to use the same program.
If WoW is indeed linear too, how come they aren't complaining about WoW doing that?
The quests in world of warcraft are a completely optional path to progression. The quests do not stand between you and your friends at the level cap.
Quests are a fast way to level up, but there are plenty of other things available to do.
There's also enough quests in the game that your can do different sets of them on different characters. Playing different linear quests is more fun than replaying the same linear quests.
Are World of Warcraft quests linear?
In the sense that each quest tells you want to do, and completing quests open up more quests in a "quest chain", yes.
However, there are some elements in World of Warcraft that mitigate the linearness.
- Quest layering: generally you're given 2-3 quests at the same time in the same area and you get to choose what objectives to go for first. This is an opportunity to try to optimize and it adds variety to the tasks.
- Distractions: gathering skills and mini-pet combat break up the quest grind.
- Alternative scenary: At most level ranges, there are 2-3 different zones you can go to for at-level questing.
For starting players, some advice. As races have been added to the game, the starting areas have gotten more and more linear. The starting quest sequences for Worgen, Goblins, Pandaren and Deathknights are very linear and are not optional. If linear questing is something that bothers you, avoid those areas.
Best Answer
Since Warlords of Draenor, there have been multiple Hearthstone reference added to the game:
Thus, we could safely conclude that Blizzard is kind of trying to add Hearthstone to the lore of their Word of Warcraft game by implying that Hearthstone games are played mainly in Orgrimmar, Stormwind, Stranglethorn and Pandaria (out of the four boardgames currently availables).
But those are still easter eggs at their current states, as we've never actually seen NPC playing Hearthstone in the game. It seems a bit weird that the common NPC would be playing as Jaina against Thrall, using demonic and draconic entities. (But Blizzard's NPCs are always a bit off so it's a possibility nonetheless.)
It's more of an opinion-based at the moment but I'd say it would be accurate to add this in a Role Play lore or assume people are playing Hearthstone in Stormwind's inns, thanks to the easter eggs added by Blizzard.
EDIT
Thanks to Michael Hampton for pointing that out: there's a game actually being played between Merra Finklestorm and Waina Steelpaw in front of the Shrine of the Seven Star (and probably at the Horde counterpart too). We can't talk to them but they sometimes let out things like "I need to rebuild my deck". There's probably other players in other cities too.
And as many have said, it's not stricly speaking "a game within a game" which could be played through World of Warcraft, but it is nonetheless a game that does take place within the World of Warcraft universe (which was the original question the OP asked for).