Windows 10 still available in boot option after being deleted

Hello,
I recently bought a new laptop with no OS, so i decided to install windows 10 on it using the windows 10 tool, but because of my excitement to install fast windows, i didn't realize i was installing it on the HDD having a SSD.

After researching i saw a solution which said to install windows 10 on SSD and from there wipe the HDD, and that's what i did, except that when i turn on my laptop, there are two options of windows 10 (the one on the SSD working and the one on the HDD that doesn't work).

Besides when i enter the good OS, there's a bug that won't let me in (login screen) so i have to restart and get in again to make it through the login (everytime).
I cleaned the HDD with CMD option, i also tried with EASEUS program but nothing worked, i also changed boot options order on the bios but that only puts the "good" OS on the top of the list.

Also, i face privileges problems on a lot of files, when i try to move them it says i don't have privileges, i've already tried owning the file, giving me all privileges (admin) and even creating a new account and give all privileges too, nothing worked, i hope that have something to do with the problem above.

It's been almost 2 days i've tried everything, i'll try gparted program too but i doubt that'll fix the program, does anyone have any idea of what to do?? even if that implies wiping all disks to start all over, as long as it works!!

Thanks for your opinions.

Connect only the SSD (and DVD drive if you need it). Leave all other drives disconnected. Boot the computer from a Windows 10 installation USB flash drive or DVD. When the very first screen comes up, press Shift + F10. In the command Window that opens, run the following commands to completely erase the SSD:

diskpart
select disk 0
clean
exit

Then proceed with the install, when asked, select the custom install option. You should see nothing but unallocated space on the SSD. Highlight that, click next to let Windows set it up. After you get Windows 10 installed and booting from the SSD, then reconnect the HDD and do what you want with it.

I though about it but its been less than a week since i have this pc, and that would brake the warranty, and when it comes to hp you don't know what can happen.

Sorry, I see it's a laptop and sometimes inconvenient to disconnect one drive. The biggest reason for disconnecting the HDD during install is to make sure that the boot files don't end up on it. So, due to your file permission problems, it's still a good idea to start over. Do you want to start completely over from completely empty drives? Assuming you do since you mistakenly installed Windows 10 to the HDD first.

Make sure the computer is set to boot from the SSD first in UEFI settings. Then use the boot override menu to boot the computer from the Windows 10 USB flash drive or DVD. Again on the first screen press shift + F10 to get into command prompt. Erase both drives with the following commands:

diskpart
select drive 0
clean
select drive 1
clean
exit

Select the custom install option. This time make sure to highlight the unallocated space on the SSD, then click next. Windows 10 should then only set up the SSD and install Windows 10 there. Once that is done, then you can create your data partition on the HDD.

Before you type select drive 0 above, if you want to see what drives are listed you can run the command "list disk" (without the quotes). The SSD should be drive 0 and the HDD should be drive 1.

If you don't want to fix the file permission problem and just remove the second Windows from the boot menu, then in Windows run "msconfig" (again without the quotes. Select the boot tab. There you can remove the extra entry from the boot menu:

Thanks for your help.
For the file privilege problem what i did was a manual copy of the files i did in the HDD windows to the SSD, then cleaned the HDD and moved them back, as for the boot problem, your solution worked very good thanks! but i still have a problem, when it enters the screen with the hour on it, i click on it and it gets stuck right before entering the login screen, it shows only the background with some opacity, i still can acces the buttons of the southeast corner so i press restart and after restars it works normally, i have to do that everytime i turn on/leave hibernation my laptop.