Can a band continue to move after a new avatar joins?
Yes, if it still has movement points (MP). Remember, the MP of a band is the lowest of the MP of all members of the band. So, if a band had 5 MP and is joined by an avatar with 2 MP remaining that turn, the new band will have only 2 MP. Here are some examples:
Ex. 1: joining a band
Band X has 6 MP and avatar A has 7 MP. Band X spends 2 MP to move into a forest hex and holds their movement/reserves their action. Avatar A spends 5 MP to go through a swamp hex and then enter the same forest hex as band X. Avatar A joins Band X. Prior to avatar A joining, Band X had 6-2=4 MP remaining. After reaching the forest hex, avatar A has 7-5=2 MP remaining. The new band -- Band X + avatar A -- now has min{2,4}=2 MP remaining this round.
Ex. 2: leaving a band
Band X has 4 members (Avatars A, B, C, and D) and starts on a Mystic's hex. Avatar A decides to remain with the Mystic and get a potion brewed, so does not make a movement roll (remember: if you stay where you are, you do not roll movement and fate!). Avatars B, C, and D roll movements and get 4,6, and 9 respectively. If avatar D (9 MP) decides to leave the band and strike off on his own, avatar D would have 9 MP and the remaining band (avatar B and C) would have min{4,6}=4 MP. If avatar B decides not to stay with the band, the remaining band (avatars C and D) would have min{6,9}=6 MP. Staying with/leaving the band must be decided before the band starts moving. Once the band begins moving, each avatar in the band locks their MP to the band's MP (so the band B,C, and D can't use 2 MP and then have avatar D leave and "revert" back to 9 [original] - 2 [band moved] = 7 MP).
Can avatars move on half hexes?
Yes
How do Shadows move in the Shadow Realm?
Shadows move randomly in the Shadow Realm. The easiest way to determine where a Shadow moves is to pick a hex adjacent to the Shadow and call it "1," then proceed clockwise around the Shadow calling the hexes "2," "3," and so on. After the hexes have been numbered "1" through "6," roll 1d6 to see which hex the Shadow moves onto. If the Shadow would move on to a hex that is not on the land mass, re-roll the 1d6.
What does it mean by Shadows "move directly toward the nearest stronghold"?
Shadows take the shortest path when moving to the nearest stronghold. When in doubt, roll a die for the Shadow's choice of path.