For (1), you are correct. AWBWT should be multiplied by the time spent on all activities eligible for the Well-Being module. For (2), if you are using one observation per Well-Being module respondent, along with their average affect during a certain activity, then you should use the WBWT weight for your multivariate analysis.
To summarize, use the AWBWT method described in the previous answer, modified as mentioned in (1), to generate your average affect. Then, use the WBWT weight for your multivariate analysis of this average affect.
Hope this helps.