Excluding variables does just what the name implies - it excludes them entirely from the analysis. Usually this is used for items we included in the dataset, but do not want included in the model.
For instance, I'll sometimes manually add an "attribute" to an alternative-specific CBC design that is a placeholder for levels that are entirely correlated with the levels shown in another attribute. I want to show the levels, so they appear in the design, but they don't actually vary independently so we don't need them in the analysis.
Another reason we might exclude a variable is if it was not chosen often enough to get a good read on its impact. This is especially true in MBC, where we might include menu items that just don't get selected very often.
For your binary variable, if you've coded it as 0 and 1, you would probably set it as "linear". If you've coded it as 1 and 2, then you could set it as "part worth" or "linear".
