Yes, they are cross-effects. And, yes, they carry a value on the same row (in the design matrix, when you Preview Design) as the row they affect.
Remember, our MBC software automatically dummy-codes...where for a binary attribute, an index of 1 is associated with "not available" (the "reference=0" state) and an index of 2 is associated with "available" (dummy code="1" state). So, when the availability variable takes on an "available" state, you should get a large positive value for the beta associated with the availability variable.
Once you've got it set up right, the simulator will still predict a share for a non-available product...but that share should be very, very near 0%. (If it isn't exactly zero, just ignore it and re-normalize the other shares to sum to 100%). So, it isn't necessary to try to remove the rows associated with missing products.
This gets into very advanced areas, for which there are multiple ways to do things. Since MBC is an advanced analytical-end product that offers an open "sand box" with multiple ways to specify the models, we cannot provide full support on modeling issues through the course of our free technical support line. Hope these hints can get you going on a good path.