1.During the movement of the traveler, it seems possible that the traveler cannot move to a location because there are no pieces of the appropriate color on any routes where the traveler can legally move to. What happens in this case?

2. On page 3 of the rules, under the possible bonus opponent actions(#2), it seems that something is missing or I am reading it wrong. If you meet the conditions for bonus (color tied or more T/M on route, or empty space on route) and there is another color space on the route and an empty space, is it the intent that you place a T/M on the empty space or get a point? From the rules on pg 3, it seems that you get a point, but in the example #3 on pg 6, it says to place a T/M. I played that you place a piece as long as there was any empty space on the route and the turn's color wasn't in a minority and it seemed to work, just wondered what the intent was.

3. The restriction that all opponents combined may have no more than 1 merchant on any route seems violated by the game setup when it is possible to start with 2 merchants on the route to Coellen. Is this restriction meant not to apply to Coellen at all and can you place more than 1 there later or just during initial setup?

4. Regarding the Liber Sophiae for the opponent; you cannot use it unless you complete the route that you move pieces to, but are you allowed to move pieces to more than one route as long as you complete at least 1 of the routes?

Answer#1 The only way that I could see this happening is if a color only exists on the board in dead end routes. The traveler must travel as many routes as needed to reach the turn color even if this is across the board. Don't set that up. I am not even sure if it is possible because of the cost that may arise as the moves become more and more expensive to make. Rule 1.a and b on page 3 only states that you are required to pass through 1 city. There is no top limit.

Answer#2 You would place a marker if it is the only color on the route, there is an open space and the color is not in the minority which is the case on the example page that you cite (last page). The game scores a point for a minority condition and a full route or a full route of the color whose turn it is. I don't know if this is clarifying your question. If you follow 2.a.i.1, 2 and 3 in order it is acting like a flow chart to determine the game's bonus action.

Answer#3 Only during setup does this apply except as you note what might occur with the Coellen route as a merchant may join a cube on the 2 player board. See 6.a.iii as a reference. This will not happen on the 4-5 player side as the Coellen route is only populated with merchants. See 6.a.ii.
During the game you need routes to fill up with like colors otherwise the game will run out of hardware in short order. You want the game to finish routes to open up your tableau and to get more cubes and discs for the game. This is a delicate balancing process and a key strategic point.

Answer#4 The Liber Sophiae action can only be chosen once per opposing turn 4.iv.1 on page 5. The traders or merchants may come from different routes but all routes that receive a trader or merchant must be completed this turn. I would tread lightly on completing multiple routes for the game as this potentially can give up too much position. This was proven to be a necessary restriction during playtesting. I figured out how I could take advantage of the action to the detriment of balanced play.

In the example #3 it is purple's turn and the route is red-empty-purple.
Here is how I understand the rules as written and maybe you can help me understand.
1st, check to see if there is a bonus. In this case there is because purple is tied with or has more T/M on the route than any other color. It also qualifies because there is an empty space on the route.
Check 2.a.i.1: There is no further T/M of another color as purple is on the last space, so move to 2.a.i.2.
Check 2.a.i.2: If there are no other colors on the route and there is an open space, place a T/M on an empty space either in front of or behind traveler. (Fails in this case because there is another color (red) on route)
Check 2.a.i.3: If the route is full of color's T/M (no) or the color is in minority (no) or a differing color is behind traveler (yes) the game scores a point.
Thus I have this as the game scores a point, but in the example you have purple place a T/M.

What happens in this case? Purple's turn and the route is purple-red-empty.
There is a bonus.
Check 2.a.i.1: There is a different color marker in front but there is an empty space, so this fails.
Check 2.a.i.2: If there are no other colors on the route and there is an open space, place a T/M on an empty space either in front of or behind traveler. (Fails in this case because there is another color (red) on route)
Check 2.a.i.3: If the route is full of color's T/M (no) or the color is in minority (no) or a differing color is behind traveler (no) the game scores a point.
So in this case all 3 seem to fail.

Not sure you understood the question. It can occur on both sides of the bard during setup if there is a disk of the active player on the Liber Sophiae track as this allows 2 merchants (1 of each of the other colors) to be on the Coellen route. My question is can additional opponent merchants be placed on the Coellen route later if there is at least 1 opponent merchant there (making the Coellen route a permanent exception to the restriction)?