There is a way to search for tags with parameters, such as #due(today). This search term can be saved as overview, but the parameter ‚today‘ will be fixed to the date of today (when I created it). So if I pick this overview search tomorrow (1 day after creation), I get yesterday’s assignments. So I cannot currently create overview searches like #due(today), #due(next 7 days), #due(next 1 month), #due(tomorrow) to filter all notes with #due tag. This is a basic function which is absolutely necessary to not have to search by hand all the time.
What you describe is indeed not yet possible, the moment you enter a tag the date gets fixed. It is possible with the assigned date of the note (by clicking the calendar icon next to the note title), you can create smart overviews for those. We hope to add the improvements you suggest indeed.