is there a way to get the actual paths itself - instead of the distance -
from the search algorithms like e.g. dijkstra_search?

As a related question, in a weighted adjacency matrix, how are the weights
interpreted for dijkstra and centrality functions (pagerank, betweenness
centrality) that rely on it. Is it low weight = easier to "travel", or is
it the other way around?

Otherwise you can write your own search visitor which records the path
for you.

As a related question, in a weighted adjacency matrix, how are the
weights interpreted for dijkstra and centrality functions (pagerank,
betweenness centrality) that rely on it. Is it low weight = easier to
"travel", or is it the other way around?

The weights are always _minimized_, unless otherwise stated. Note that
in Pagerank the weights are used differently, since there is no shortest
path computation in this case (see its documentation for more details).