The answer to your first question is yes, filters are going to work correctly. The filter context is composed of filter from dim1 and dim2. And it propagates automatically in your situation.
Filter context is automatically propagated from the one side of the relationship to the many side, whereas it is not propagated from the many side to the one side.
As for your second question, the use of cross filter or bi-directional filter is used when you measure is defined in the one side of the relationship (In a dimension table) in this case the filter does not propagate automatically and there for you need to use cross filter or bi-directional filter.
CLICK HERE to find out more related problems solutions.