Welcome to the forum! 
First of all, the partition in question has a vfat filesystem on it, and vfat is not a UNIX-compatible filesystem. It does not store file ownership and permissions, so the permissions are faked in the kernel’s virtual filesystem layer at mount time and apply to the whole filesystem. They cannot be altered.
Secondly, if you have Fast Boot enabled, then Windows will not properly shut down its filesystems, and then the Linux kernel will interpret this as if the filesystems are damaged. That’s why it will mount them read-only, so as to prevent further damage.
The solution is twofold…
- Switch off Fast Boot ─ both in Windows and in the UEFI firmware; and…
- Add a record for the filesystem to
/etc/fstab, so that it will be mounted statically instead of through theudisks2framework.
Open up a terminal window, and issue the following command… 
lsblk -o UUID /dev/sda2
Write down the UUID for the partition. Now issue the following command… 
sudo mkdir /mnt/vfat && sudo nano /etc/fstab
Add the following line to the file, but replace the placeholder by the UUID you just copied… 
UUID=the-UUID-you-copied /mnt/vfat vfat auto,nofail,uid=1000,gid=1001,fmask=0000,dmask=0000,umask=000,shortname=mixed,showexec,utf8 0 0
Save the file with Ctrl+O and Enter, and exit the editor with Ctrl+X.
If you reboot now, then the filesystem will automatically be mounted at /mnt/vfat, and it will be world-writable ─ i.e. rwx for all users.