I'm hoping I'm understanding you. Here's what may be happening for your first question:
You say you have three separate dependent variables to predict. That means that each of those got its own model to predict what happens to it if certain variables on the menu change. So, if you change independent variable 1 (say, it's Price for item A on the menu), if independent variable 1 is only involved in the model for predicting item A's choice, then the share of choice for items B, C, etc. won't not be expected to change when price for item A changes. But, if the models you have built for predicting item B, C, etc. also involve Price for item A as a predictor variable (as a cross-effect), then choice probability for B and C should change due to changes in Price A.
Regarding what you're observing about the filter in the simulator, the only thing I can think of that may be causing the behavior you see is that you are running aggregate logit models rather than individual-level HB models. To get the filters to work interactively within the same market simulator (at least the Excel-based ones our MBC software exports or the one built-into the MBC software), you need to be working from individual-level HB models.
If you are working from aggregate logit models and want to use filters (male vs. female, for example), the way to make that work is to do an aggregate utility run with Males only turned on (using the filters)--which creates a utility run which you should name to identify it later as males only; then to repeat the same for females, re-run aggregate logit and then rename that second run to identify it as females. Then, to create a simulator for males only, you need to select the male-only utility run to be used. To create a simulator for females only, you need to select the female-only utility run.