Can you plane bamboo with a BCTW plane?

Unfortunately, bamboo is a material that is very difficult to plane with any hand tool or machine in general. It would require to be precisely cut to avoid splintering and splitting. Carbide blades are preferable for working with bamboo as you'll need the blade to stay sharp as possible when working with bamboo materials.

Why does the orange handle insert move on Try Squares?

The orange insert in the handle is a separate piece that has a little bit of movement as a design feature by John Economaki and is not a defect.

All of the try squares by John Economaki have this type of movement in the handle's orange triangular piece. The slight bit of movement promotes a more comfortable grip than a more rigid insert, although this is subjective to the user.

The main advantage to having the insert be a separate piece is that it is removable/swappable and in the event that the orange triangle were to ever get damaged or develop a burr, this part is able to be swapped out with a new triangle for a more comfortable grip.