The client was broken after yesterday's update, a client restart should fix everything
Wield a staff, set spell on autocast, click Load Worn Equipment on the GUI, choose a name for the gear preset, and then select this gear preset on the right side of every quest you want to use it on
Those quests are not supported yet
I'm afraid I'm not currently doing trials
It is likely missing a requirement; Make sure you have completed Plague City AND unlocked Ardougne teleport by reading the scroll you receive at the end of the quest