Can one say single decades of the rosary independently throughout the day followed by the closing prayers, or does it all need to be said at one time to count as a daily rosary?
If so, is it alright to say those decades while you are doing some mundane rather routine chore like mowing or doing dishes, folding laundry etc, where one is still thinking of the mysteries but they are not giving it their absolutely undivided attention as they would on their knees in prayer? I have heard of religious saying their rosaries or hours as they walk in a courtyard or garden, and they must divide their attention at least somewhat so as to be aware of their surroundings as they walk. Thanks.

Padre Pio prayed MANY rosaries per day.
The only way he could accomplish that was to pray while he worked, ate, etc.

Nuns would pray their Office while they walked in their yard as you mentioned, this was a common practice.  You even see it in the movie Song of Bernadette near the end.

Praying a decade at a time is a great way to lead you to 15 a day!

Keep it up.

I try to pray the Rosary on my knees once during the day, but I also pray the Rosary when I am walking around.