Am I right about the differences between Floyd-Warshall, Dijkstra's and Bellman-Ford algorithms?

I've been studying the three and I'm stating my inferences from them below. Could someone tell me if I have understood them accurately enough or not? Thank you.

1. Dijkstra's algorithm is used only when you have a single source and you want to know the smallest path from one node to another, but fails in cases like this

2. Floyd-Warshall's algorithm is used when any of all the nodes can be a source, so you want the shortest distance to reach any destination node from any source node. This only fails when there are negative cycles

(this is the most important one. I mean, this is the one I'm least sure about:)

3.Bellman-Ford is used like Dijkstra's, when there is only one source. This can handle negative weights and its working is the same as Floyd-Warshall's except for one source, right?

If you need to have a look, the corresponding algorithms are (courtesy Wikipedia):

Bellman-Ford:

 procedure BellmanFord(list vertices, list edges, vertex source)
   // This implementation takes in a graph, represented as lists of vertices
   // and edges, and modifies the vertices so that their distance and
   // predecessor attributes store the shortest paths.

   // Step 1: initialize graph
   for each vertex v in vertices:
       if v is source then v.distance := 0
       else v.distance := infinity
       v.predecessor := null

   // Step 2: relax edges repeatedly
   for i from 1 to size(vertices)-1:
       for each edge uv in edges: // uv is the edge from u to v
           u := uv.source
           v := uv.destination
           if u.distance + uv.weight < v.distance:
               v.distance := u.distance + uv.weight
               v.predecessor := u

   // Step 3: check for negative-weight cycles
   for each edge uv in edges:
       u := uv.source
       v := uv.destination
       if u.distance + uv.weight