Is it permissible for a woman observing her iddah to go out into the home's garden to clean it and water the plants in the early morning, while adhering to the prescribed Islamic dress?

There is no objection to a woman in her 'iddah (waiting period) going out to the garden of her house at any time, as long as it is part of the house and does not entail her leaving her home. If it necessitates her leaving her home, she may only go out for a necessity, and she must spend the night in her home. Looking at her is like looking at any other woman; there is no harm in her neighbors or mahrams seeing her, as long as she is covering what must be covered.