The following tutorial will allow you to enable the default Administrator. There are other ways to change the permission of an existing user and/or change the password of an existing Administrator. Those methods are not covered by this tutorial and are considered out of scope for the purpose of this question.
This tutorial assumes you know how to create an installation disk, boot to that disk, and enter WinRE which is contained on that disk. This tutorial won't cover how to do that. This tutorial does not require access to an Administrator account, the entire purpose of this tutorial is to enable the built-in Administrator account which by default is disabled.
Enable or Disable Built-in Administrator in Command Prompt at Boot
Download the Windows 10 .ISO
Within WinRE at a command prompt, type regedit, and press Enter.
In the left pane of Registry Editor, click/tap on the
- Click/tap on File (menu bar), and on
- Open the drive that you have Windows 10 installed on, and browse to the location below.
- Select the SAM file, and click/tap on Open.
- In the Load Hive dialog, type REM_SAM, and click/tap on OK.below)
- In the left pane of Registry Editor, navigate to and open the key below.
In the right pane of the 000001F4 key, double click/tap on the F binary value to modify it.
In line 0038, change 11 to 10, click/tap on OK
Close Registry Editor and the command prompt.
Click/tap on Continue to startup back in Windows 10.
Related Question: Where can I get a clean ISO of the Windows 10 Anniversary update?
It is absolutely necessary to reset the BIOS password.
In most cases, to remove the BIOS password one must disassemble the laptop and locate either the CMOS jumper or the CMOS battery. With the battery and AC adapter disconnected, remove the CMOS battery or if there is a CMOS jumper (3 prongs with jumper on 2 often nearby the CMOS battery), move that jumper to the CLR or Clear position, hold the power button until the power cycles on and off and or hold it continuiously for 10+ seconds. After, replace the CMOS battery or reset the CMOS jumper to the normal setting (not CLR). You can now replace the battery and plug in the AC Adapter. If you don't want to deal with the hassle of dissasembly, using a backdoor password put in by the Motherboard's Manufacturer is appropiate. Of course, this would require knowledge about the motherboard's model and brand (which still may require disassembly). At this point, the BIOS password should have been removed.
Now you need a correctly made boot USB, that is allowed by the BIOS or (if you have it) UEFI firmware. Most laptops nowadays, if by the OEM as Windows 8 or 10, are UEFI laptops. If you are infact using a UEFI firmware BIOS, you need to disable "Secure Boot" (and if possible, enable "Legacy Support") found in the BIOS settings. I recommend using a utility called Rufus to properly put Windows 10 ISO on the flash drive. If you are using UEFI in Rufus you would select UEFI and GPT, otherwise then after not being able to boot up try BIOS and GPT, then lastly BIOS and MBR.
It should then be a peace of cake to Install Windows 10 knowing that you have done it before. Of course, you ought to wipe or format all the partitions on the hard disk.
It depends on whether or not the installer does anything that requires administrative rights on the operating system.
If it does, then no, you can't install it without admin rights whether that's with the account that you're using or running it as an admin or a different user.
If it doesn't, then yes, you can install it without admin rights. I don't know if this is true today, but it was possible to install CC Cleaner under Windows XP or Windows 7 (can't remember which) without admin rights. I'm a Linux Systems Engineer right now and haven't done Windows desktop support in a while but I believe it's possible to install the software for Xerox's printers without admin rights in Windows 10 (at least it was in Windows 7). Some of the other printer software allows it to be installed without admin rights.