Is there anywhere in Stelida to buy breakfast provisions
In stelida you will find a Koutelieris supermarket which is part of the European Spar group, it is located near the beach of Agios Prokopios, there are other Koutelieris on the island including 2 or 3 in the town of Naxos
https://maps.app.goo.gl/CLiPmY45kh1719VA8
There is also a large AB supermarket in Naxos town
https://maps.app.goo.gl/CVRzSRaBDh6iDpcD9
Since you are self-catering, after numerous stays (probably more than 200 nights) spent in self-catering accommodation in Greece, what I recommend is:
Tip 1: Wait until you are in your accommodation before going to do some shopping. There are often basic ingredients left by previous guests or provided by the owner. It can be coffee, sugar, oil, butter, drinks, etc. There is no need to purchase thinks that are available in the accommodation .
Tip 2: There are now often espresso coffee machines that accept coffee capsules from specific brands.
If there is one, there should be a few capsules left. Look carefully at the model so that you can buy the same model in the supermarket
Tip 3: For bread, prefer bakeries to supermarkets.
Tip 4: When we go to the islands, we take a large supermarket bag with us. It takes up little space in your luggage and is always very useful.
Do most local restaurants require reservations
In more than 30 years of staying in the Greek islands in May, June, September or October (never in July/August) we have only reserved a restaurant for dinner once, and it happened to be on Naxos. Not in Naxos Town. It was at "Apolafsi"
http://www.apolafsinaxos.gr/
That being said, if you go to the 3 or 4 restaurants in Naxos Town most recommended on Trip Advisor there is a good chance that you will meet dozens of other tourists who thought they had the same good idea as you, probably by herd instinct. :))
One of the benefits of having a car is that you can avoid this kind of situation.
In Paros we do not plan to rent a car.
Big mistake!
You can also go to Lefkes and Naoussa and many other places very easily by bus. The bus network is excellent in Paros. All buses depart from Parikia. However you will always be dependent on lines and timetables.
No, it won't necessarily be easy to find a taxi, and taking 4 taxis a day will cost you more than a small rental car.
However, can you also just spread out a towel if you would rather?
Of course!
Especially since last year there has been a movement to free the beaches from these horrible rows of sunbeds and umbrellas. This movement began in Paros and Naxos where some beaches was almost no longer accessible because they are invaded by these sunbeds, often installed illegally.
https://www.bbc.com/travel/article/20230912-what-to-know-about-the-beach-towel-revolt-taking-back-greek-beaches
The "Save the beaches" movement in Paros: https://tinyurl.com/3hrrdcrj
Following these protests the Greek government has finally decided to act more firmly and has published new laws this year which should restrict the spaces occupied by sunbeds and help return the beaches to everyone.
https://greekreporter.com/2024/03/15/greece-new-beach-law-bans-sunbeds-beach/
So bring your towels and don't forget that the shade of the Tamaris trees is free
Regarding the beaches and many other things to do and see in Naxos I made this map:
https://www.google.com/maps/d/edit?mid=1d7GZMjFODUlB8lf7EPSXQRwu-YXaKxw&usp=sharing
And for Paros:
https://www.google.com/maps/d/edit?mid=16DROB8mBOLkd8HdwFG522SnH0-MmiI8&usp=sharing