The more a non-diatonic chord resembles a diatonic chord the less friction it will create, but strong rules don't seem exist. Apart from the initial dissonance you get when jumping to a severely out-of-key chord you can always steer it to wherever you want and resolve it. It's just a question of how much 'friction' you are willing to use in your first jump. The 'roadmap' you give is not as much a set of rules as it seriously demand the user of it to use his/her own ears and judge whether or not it makes sense. For example, if you go to A-major in the above table then you might chose to get back to the blue chords without using Dm. Might take a little longer but it's up to you to decide what's acceptable and what is just too bizarre.
I was looking at this map and was looking at the green bubbles, for example, the A (secondary dominant, i suppose?) and C#dim7 leading to the Dm. I'm thinking the reason C#dim7 is on there is because it shares two notes with the A. If that's the case then can't I use a C#m6 and many other chords as long as it leads back to Dm smoothly?
The C# dim 7 is there, not only because it shares two notes with A, but because its root (C#) is the leading note of D and its fifth (G) forms a tritone with the root. That puts it in a strong dominant relationship with D min. The tritone between its notes C# and G can resolve naturally to D minor's D and F. Using C#m 6 instead, means the G would be G sharp and you'd lose the tritone, which would weaken the dominant relationship to D minor.
Spot on, Fretsource.
I have always thought of such chords secondary vii chords in the same way the A would be a secondary dominant (V).
If you want to be good, practice. If you want to be great, you must constantly change the way you think.
No, your conclusion is fine. It just depends on what you want to do. C#dim7-Dm7 would sound more 'fininished' then C#m6-Dm7 but whichever is better depends on what you're doing. You might even, if noone was looking, get away with using both after each other: (Bbm7/5b-C#dim7)-Dm7. By switching C#m6 for Bbm7/5b you get a nice bassline into Dm as well.