Skull threshold is the lower threshold hold and scalp threshold is the upper threshold.
The label values represent an arbitrary numerical value that a specified voxel will take on. For example, any voxel that has a label value of 16 will be considered/labeled as scalp in BrainSuite. You have the option to set this integer value.
To save out the surface files, you have to run the Skull and scalp step in the Cortical Surface Extraction Sequence dialog (Cortex -> Cortical Surface Extraction Sequence dialog). Make sure that the “save output of each stage automatically” box is checked (autosave is default). If you already have the structural file and brain mask (fileprefix.mask.nii.gz) loaded, then you can uncheck the Skull stripping step and just run the the Skull and scalp stage.
You can also run this via command line, with an additional -s flag to have the surface outputs as described here.