1. I am not sure what your concern is with the injected field and waveguide dimensions. If your field is much larger than the waveguide and you inject inside the crystal and some of those wavelengths are in the bandgap then you are dumping power into the crystal that cannot go anywhere which will be problematic. If you want to use the larger field inject from outside.
2. When you open the 2D or 3D Simulation dialogs (seen in the tree on the left side of the product) you have options to change the “Mesh Delta” for X/Z (2D) as well as Y (3D). You have the auto check on these so the mesh will be automatically set to lambda / 10n where n is the highest index material in use. For your design this corresponds to only 4-5 points across one of your rods and only 2-3 points between rods. You will want to run a series of simulations with smaller mesh sizes to see how the mesh affects the results. There will come a point where the results stop changing.
3. This is not a simple question as there are a broad number of variables here such as lattice spacing, rod radius that also impact your band structure. Additionally you could look at removing more than one row or using different radii for the rows that are bordering the waveguide. There are many papers out there on design options for PhC waveguides.

Scott