Hi Nassim. I'm Greg, an installation specialist, 10 year Windows MVP, and Volunteer Moderator here to help you.
"On Windows 10, similar to previous versions, the folder is located in C:\Users\Public, and by default all user accounts on a computer have access to it. However, depending on your network configuration, you’ll be limiting access to only network users who have a password protected account on your computer." More about this here:
https://pureinfotech.com/public-folder-share-fi...
If that's not it then having both hidden Public folder and especially Read Only sounds like a corrupted User account, which we see here every day. To test this create a new Local Admin account, sign into it, test if the problem persists. http://www.howtogeek.com/226540/how-to-create-a...
If not move your files over, check all programs run from it or reinstall them as needed,
Then when ready delete the old account: http://www.howtogeek.com/226540/how-to-create-a... You can then link your MS Account in Settings > Accounts > Your Info > Sign in with MS Account instead, if desired.
I hope this helps. Feel free to ask back any questions and keep me posted. If you will wait to choose if I solved your problem, I will keep working with you until it's resolved.
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