fat32 | Tiny FAT32 file system implementation | File Utils library

Depending on the installation, the root partition might only use a part of the logical volume (LV).

Try the commands vgs and lvs to get information about your current setup. I assume that vgs shows about 30G free space. You can enlarge the root volume using lvresize. After this you need to adapt the file system. This depends on the file system type you are using. If you use extX then you might want to run resize2fs.

Edit based on the edited question:

Yes, everything can be done when the disk is mounted and in use.

BUT YOU NEED TO TAKE CARE ABOUT THE COMMANDS YOURSELF!!! A WRONG COMMAND MIGHT DESTROY YOUR SYSTEM.

PLEASE TAKE YOUR TIME TO MAKE YOURSELF COMFORTABLE WITH LVS BEFORE CHANGING THE SYSTEM.

There are many good tutorials which might help you, e.g.:

http://ryandoyle.net/posts/expanding-a-lvm-partition-to-fill-remaining-drive-space/

There's no BPB in the MBR. You are mixing two types of bootsector.

The MBR (Master Boot Record) is the very first sector on the disk. It contains partition info in its partition table that starts at offset 01BEh. In this kind of bootsector, the first 446 bytes (512-64-2) are available for the bootsector program whose task it is to load the DBR.
The DBR (DOS Boot Record) is the first sector on the partition that was set bootable from the partition table. This kind of bootsector does contain a BPB (BIOS Parameter Block). For FAT32, it occupies the first 90 bytes. Considering the mandatory bootsector signature at the end, you have 420 bytes (512-90-2) available.

I have no idea how to make that program, disk related stuff is too hard and confusing for me

That's too bad for someone that wants to create their own OS.

The BPB is too large and if I copy it then my bootloader code wont fit in 512 bytes

You'll have to optimize your code for codesize. The required structures are what they are.

I don't know what parts of the existent MBR code I should copy

First copy the existing DBR from disk to a file eg. 'MyDBR.bin'. Then write your bootsector like this (FASM):

UWP application unable to access USB drive even though permissions are set

Directory.GetFiles can't not use to access file with path in UWP platform. And you can only use Windows Storage API to access file with path (enable broadFileSystemAccess ), by the way, System.Management Namespace is not work for UWP platform, and if you want to format USB device within UWP app, please use desktop extension to process. for more please refer stefan' blog UWP with Desktop Extension

You need to change the size of your partition with fdisk before using resize2fs: delete the current partition and create a new one that starts at the same block as the one you deleted.

For example:

Thanks all for the comments.

So I figured out a way to work around this problem (in Windows 10). The workaround is to lock, dismount and create disk as GPT to make Windows think it's unallocated disk. For whatever reason if it was formatted as FAT/FAT32, I just wouldn't be able to WriteFile to the card.

The following is the example code that is working for me:

The point about anonymous type, is that you don't have to give them a name, the compiler will do it for you.

<>f__AnonymousType0 is not a valid name in user code, but looks like the name generated by the compiler. You can't use it.

Just use anonymous syntax :

It may take time for kernel to be notified about partition changes. Try calling partprobe before mkfs, to request kernel to re-read the partition tables.

Solved the issue. As the boot files were installed in /boot, but the bootloader was installed in /boot/efi, the relative path was the latter rather than the former. Solved it by copying the boot files to a dir inside /boot/efi

Nothing wrong per se. The boot partitions are usually separate for security and recoverability reasons (plus they sometimes need to be a "simple" filesystem type like FAT).

You can increase the size of the logical volume to the full 10T using LVM tools: