Anybody know any good ways to pass time when waiting for missions to finish? :/

If you don't want to splurge on buying items XD then I recommend splurging on breeding & battling. Breeding is a great way to pass time because the possibilities are endless. I also recommend battling, maybe you can train some of your other slyestis while the ones you use mainly with your party are on a mission. I also recommend going on the forums lol, just like I am now. Hope I helped!!! Ooh and watching Netflix too... Except i think you meant on Sylestia... :D

Mass nurture! Always fun + you get essences sometimes.

my answer's probably late lol

you can finish the storyline up to Astryl's Tranquility! you can follow the battle guides and get a team to fight all the way through the story. I think it's a good thing to square away, especially since you have to have the storyline up through Astryl's Tranquility to access the Mega Zone in the future.

Nurturing is fun imo because you can buy things from the scale shop, like eggs that cost over 2200+ scales, and sell for money.
Grinding dungeons like the Dungeon of Forsaken (which you'll find at the end of Umbra Forest) can also net you gold and possible mythical items (the current top-tier gear until Mega Zone comes in).

Grinding higher level areas in general (ie Astryl's Tranquility is lvl55-60) can get you gold, excess equipment (which you can sell for gold) and possible loot from the bosses inside (which you can also sell for gold, or keep for yourself).

Good luck!

What happens when a mission ends? I sent 2 of my sylesties on missions,and it said 1-2 hours...it's been 3 days and it says I can't breed those sylesties because their still on a mission. Is there something I have to do?

Once the time is up, you have to end the mission manually.

To end the mission, go to Explore>Missions.
You should be able to end the missions on that page and breed your pets as normal afterwards.