Asking about HB-Reg is like asking about advice for running regressions in Excel or SPSS. Typically, with HB-Reg problems, you are considering that each row (case) is independent of the others. Thus, if you multiply two IVs together to create a new IV, that's an Interaction Effect.
Cross-effects are something different, involving discrete choice designs where multiple alternatives are being considered. The multiple alternatives are each coded as rows (cases), but they are interrelated within sets (tasks). Cross-effects model IIA violations...meaning that the utility of an alternative is not only a function of itself, but a function of other alternative's attributes. You aren't cross-multiplying IV columns to create cross effects in discrete choice modeling. You're simply including level codes for one row in the matrix that are actually associated with a different row in the matrix.
Your other question about interaction effects and problems. It's easier to interpret the results of interaction effects if the original main effects are zero-centered. That way, the coding for the interaction effects is orthogonal to the main effects...and the utilities of the main effects may still be interpreted in the traditional sense, independent of the interaction effects. If you don't use zero-centered independent variables, then the interpretation of the resulting betas is more complicated (since information previously captured by main effects is now partialed out over interaction effects).
Oh, and don't forget that interaction effects place additional demands on the experimental design. The experimental design must be able to support main effects plus additional interaction effects to be able to include them in the model. Otherwise, you'll have troubles with convergence and overfitting.