I wish to be able to fully TEST or ASSESS my Hardware (PC and Laptop) and System (Ubuntu & Windows8.1/10) and Drives (I have many) in order to assure functionality.

Great response, thank you!  Refers to what others told me also, nice and concise.  So...

First, I download:
(1) UBCD
(2) memtest86+
(3) Manufacturer's Disk Diag

Then install them?
Then run them in same order?
And just to confirm, these will work with Obuntu and Windows systems?

Well, rindi and dbrunton, thank you both. Great insights.

Thanks for the link, rindi... do I need BURNING SOFTWARE in order to burn it to a CD/DVD?

So... I just RUN the disk as the boot once I've created it, and then... do the tests?

>>  do I need BURNING SOFTWARE in order to burn it to a CD/DVD?

Yes.

>>  So... I just RUN the disk as the boot once I've created it, and then... do the tests?

Yes.

See http://www.ultimatebootcd.com/ for an overview of what is on the UBCD.  There are tutorials on YouTube on how to use the UBCD.

Here is how i do it :
Hardware diagnostic CD    UBCD

go to the download page, scroll down to the mirror section, and  click on a mirror to start the download
Download the UBCD and make the cd   <<==on a WORKING PC, and boot the problem PC from it
Here 2 links, one to the general site, and a direct link to the download

since the downloaded file is an ISO file, eg ubcd527.iso - so you need to use an ISO burning tool
if you don't have that software, install cdburnerXP : http://cdburnerxp.se/

If you want also the Ram tested - run memtest86+ at least 1 full pass,  - you should have NO errors!
 
For disk Diagnostics run the disk diag for your disk brand (eg seagate diag for seagate drive)  from the HDD section -  long or advanced diag !  (runs at least for30 minutes)

http://www.ultimatebootcd.com/                        ultimate boot cd
http://www.ultimatebootcd.com/download.html             download page

**  you can make a bootable cd - or bootable usb stick

for completeness -here's how i handle disk problems : https://www.experts-exchange.com/Storage/Hard_Drives/A_3000-The-bad-hard-disk-problem.html

Jeffereeener, time to give some feedback - how are things going?

>>  As per CV recommendation  <<  ??  what is this? i dont know that

CV = Cleanup Volunteer

ah shortening words - Always messing up things