How exactley do they work, I'm not sure what the ruling is on how they move. Characters like Power Ring and so on. I can understand moving with the front of the base, but where does the back stop, when you turn it to be horizontal or vertical does that count as a move even though the front end stays put?

From the Rulebook, p.41:
"Moving.
The player moving a double-base character chooses any square
adjacent to the double-base character to begin counting movement. A doublebase character must end its movement so that both ends of its base occupy one of the squares within its speed value and both ends of the base are on terrain at the same elevation, even when soaring. When a double-base character stops its movement on a diagonal, it occupies only the 2 squares occupied by the center dots printed on its base. A double-base character may not end its movement with a wall between the center dots printed on its base."

So, the only restriction (besides elevation) is that the "back" must be within this character's speed value (no more gaining one extra square by "tail-whipping"). Placing the "back" doesn't count as a move.

Hope that helps.

When you move, you start the count from the front (the front being the end closest to the direction you plan to move). At the end of your movement, neither piece can exceed your total movement.

Example. You move 8 squares with your transporter (full movement).

XXX
ABA
AAA

B=the end of the piece you started your movement with.
A=where you can place the other end
X=squares the other end can't be placed in.

Just imagine the double based figure is two adjacent single based figures with exactly the same dials. Any square that a single figure standing in the same square as the front end can reach legally using the dial is a legal finishing square for the front of the base.

Any square that a single figure in the same square as the back end of the base could reach legally using the movement on the dial is a legal square for the back end to finish in....as long as it is adjacent to the front end.

Okay, so what are the advantages/disadvantages to using a character like this?

Advantage is that you can tie up more figures and are easier to stay in LoS for prob etc. You can also use it to block LoS to your important figures (operation human shield!) Disadvantage is that you have a much harder time avoiding line of sight for opposing attacks. You can be shot from many different angles.

Hence, a double-based Giant (Devil Dino) is a fun pile of sitting duck.

They also cannot be "knocked back" (by any means, including Force Blast, BFCs, etc.) and cannot be TKed.

It's rare that you can reliably use this to your advantage, but there have been odd examples when I've been able to use this to my advantage (only because I pulled so many Vigilantes in JL events!)

The big advantage is to control Lines-of-Fire.

I wish they were a transporter, too. It would have been awesome to have a Transporting, Giant, Double-Based Duo to play with!

Especially since you could then yell "Dinosaur drive-by!" when making a transporter attack.
Oh well. Doublebased Giant is plenty interesting as well.

They can also be used to break adjacency between characters on a diagonal which can have all sorts of useful and amusing effects

As it is you can yell "Woah dragon...WOAH!!!!! Dang it, when I says woah, I means WOAH!!!!"

Wow...I'm old.