The Need for Seed

Construct a weighted directed graph on the $N$ towns, with a directed edge from town $u$ to town $v$ if $diff[u]>diff[v]$ and there is a road connecting $u$ and $v$, weighting the edge by the time taken to cross the road.

For Subtask #1
You can run Djikstra’s Algorithm to find the shortest path from $X$ to $Y$. We will never traverse a path where we will face obstacles because such roads were not included in the graph.
Complexity: $O(L(V\log(V) + E))$

For Subtask #2
This graph is acyclic because the total order specified by difficulty represents a topologically sorted order. Find the topological order of the nodes using DFS. Then relax the outgoing edges in the found topological order to find the shortest path.
Complexity: $O(L(V+E))$

Note that, such a path might not exist, even if $X$ and $Y$ are connected via roads.