Are you booting with UEFI or BIOS. It looks like you have an ESP - efi system partition. And that Windows boots in UEFI.
The bios_grub partition is only required if booting Ubuntu in BIOS mode on a gpt partitioned drive.
You cannot edit or modify mounted partitions. So you have to use your Ubuntu live installed DVD or flash drive to edit your partitions.
Moving partitions particularly moving left can cause all sorts of issues. Best to have good backups as any interruption of a partition move corrupts all the data.
Also do not move Windows left with gparted. If Window own disk tools let you, then maybe you can, not sure. But it will require chkdsk after any change. So best to have your Windows repair flash drive handy, just in case.
Your drive is starting to get full. Windows NTFS partitions really like 30% free space inside the partition to run well. At 10% free it gets real slow. Linux also needs some room, perhap not quite as much as Windows. Linux ext4 partitions do hide 5%, just to try to prevent you from crashing system if too full.
I prefer to use 25GB for / (root) and actually use about half of that. But I have all data in data partition. I used to also have a separate NTFS data partition when I still booted Windows XP, but now have no Windows. I kept my XP partition smaller and had a d: drive for data. That way I was not writing data into the Windows system partition which can overtime cause issues.
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