Celica +atk vs +spd

I think that depends on how you want to build her. Both viable. Mine is +Atk w/ Life and Death, and she's a nuke. Has plenty speed, so I enjoy the extra damage. Depending on your choice of A-slot, though, you might opt to go the other way.

I think it really depends on which B slot you are taking. If it's Chill Spd then +atk is better because Celica will doubles almost anything but will hit harder. If you're not running Chill Spd either +atk or +spd are good, but +spd I think is slightly better.

Distant Def is good but it's not recommended to place her in range to a mage/archer to hit her because if she loses HP she will be weaker with no profit. You should avoid placing her in fights she can't counter.
I use Fury in mine.

+atk is better. If you have a Faye, H!Jakob or LA!Roy, you can give DD to them for a triple DD Guard Bow build. (sorry my shitty english)

Mine is +spd -hp, and I run her with LnD, Chill Spd, Threaten Atk, and Heavy Blade. She procs Glimmer every round of combat with this set. +Atk will work fine with this set, but I recommend +spd just in case you face a team with multiple high speed units.