When you think through the math of what MNL does, then you realize that responses of None also can provide at least some information for utility estimation for the other attributes and levels.
Scenario 1: if you don't inform HB MNL that this respondent rejected certain concepts prior to the formulation of the relevant set, then you'll not be informing utility estimation fully about how this respondent forms preferences. In ACBC, when respondents drop levels from consideration prior to the conjoint tasks (done via constructed lists), we add synthetic tasks to the choices for that respondent showing that the respondent "saw" these dropped levels and rejected them (how we do that is described below).
Scenario 2: There are many ways to do this. The way we do it in ACBC for a rejected (dropped) level within an attribute is to create a new "threshold" parameter for this attribute that is coded as a 1/0 in the design matrix as a new column in the design matrix. If you have 5 levels of brand and the respondent rejects level 3 (and we want to inform utility estimation that level 3 should be lower than levels 1, 2, 4 and 5), then we add 5 new binary choice tasks to the respondent's design matrix. These are coded as extreme partial-profile tasks, where the other attributes are coded as zero. Level 1 of brand is compared to the threshold concept (not the None!) where the threshold concept is coded as a 1 in the threshold column and chosen. Same for levels 2, 4, and 5. But, level 3 is compared to the threshold concept and rejected. After utility estimation, we ignore (throw away) the threshold parameter associated with this attribute.
The coding in more detail is described in a PowerPoint training we gave on ACBC the year we released ACBC. You can write me directly if you want those slides and you know my email.