I have a broken Ubuntu OS. I have tried many a ways to restore/recover said hard drive. Boot-repair, Windows recovery, Ubuntu live usb repair disc option.... nothing is working. Right now I have a screenshot of what my partitions look like, mind you I'm typing this from the live USB and that may reflect one of the mini partitions displayed. Although the 750gb partition that is shown was where Ubuntu was previously installed in place of my Windows installation. Yes that is right, I installed Ubuntu over Windows instead of the dual booting option like a fool. Let us move past that. Right now I want to format my partitions so as to repair my windows OS and very soon install Ubuntu as a dual boot. Please step by step or semi-detailed instructions in using GParted or possibly the terminal. I'd appreciate any help offered and I thank you in advance]1
First, when you installed Ubuntu over Windows, you automatically erased Windows. So, it is gone and unrecoverable. You will have to reinstall Windows if you want to use it again.
Second, it is recommended to install Ubuntu on a ext4 partition, not fat or ntfs partition. You could install it on Windows-type partition (under non-standard conditions), but it works best on linux-type (ext) partitions.
The recommended way to install a dual-boot system is to first install Windows automatically (it creates some 3-4 partitions) and then install Ubuntu. Just remember: in a dual-boot environment GRUB (the Ubuntu bootloader) will supersede the Windows bootloader. If you remove Ubuntu at a later time, you will have to repair the Windows bootloader.
Keep in mind that Windows can't deal with linux partitions. Just clean-erase the entire hard-disk for now and let Windows do its' work.
Ubuntu typically uses 2 partitions: ext4 (>10GB) and swap (= 1,5...2xRAM size).