What should I do for my deceased husband and for myself after the 'iddah (waiting period) has ended, and is it permissible to say "my husband" when supplicating for him, and is my commitment to the 'iddah considered incomplete due to my going out for work, buying necessities, and visiting my sick mother?

There is no objection to a woman in her 'iddah (waiting period) leaving her house for her needs, provided she adheres to the Shari'ah limits, such as leaving for work, to run errands, or to serve her mother. As for worship, there is no specific act of worship due to the 'iddah. However, certain things are forbidden for a woman in her 'iddah, such as using perfume and adornment, and spending the night outside her home until the 'iddah concludes. The effects of these prohibitions cease with its conclusion, even if the woman did not adhere to them.