Does a pilgrim with the travel domain grant 10 feet of extra speed to everyone in the caravan bond? If so, does this last all day?
Ka-bump.
At 1st level, by leading a group prayer for 1 minute, a Varisian pilgrim can select a number of traveling companions equal to her cleric level + her Wisdom bonus. She may use her domain-granted powers on any of these traveling companions as if they were her. She can use these abilities on her traveling companions at a range of up to 30 feet, even if the ability normally requires her touch.
The 10 feet of speed isn't a power that you use, it's just added to your character. Similarly, a Pilgrim with the Knowledge domain would not grant class skills.
You could let your allies ignore difficult terrain or teleport, though.