There is one certain way to tell if a civ is dead, and that is to embark and check the civ screen's civs. If the civ is merely struggling you'll find your own civ listed, quite possibly with the message that there are nobody upholding any important positions. If the civ is truly dead the screen is blank, i.e. no civs listed until another civ is encountered (caravan, siege or kobold theft attempt) at which time you'll get your own plus the one encountered.
If you've got more than one dwarven civ to select pre embark they're most likely not dead, as DF culls dead civs unless all civs are dead.
If your civ is "merely struggling" you get a monarch at the two year mark at the latest (usually earlier). You'll also get a dwarven caravan and a third migration wave, both of which shows the civ is not dead.
Legends mode can give you some indication if the status, although it can only show you the civ is in a bad shape. No dorfs left will cause void dorfs to arrive in the migrant waves (2 waves for dead civs, unlimited for "struggling" ones).
There is no way to get a monarch immediately, although struggling civs can get them soon after embark (with a higher chance if the position is not filled at embark), but I don't know what/if triggers a self appointment of a monarch. Conflict might trigger it, but I've also had cases where killing DF and replaying from the last save resulted in the self appointment while the one killed didn't, despite playing it basically the same way.