Hard drive replacement iMac late 2013 I know almost nothing about computer repair. I'm an elderly woman who is partially blind. I did find a step by step guide on iFixit and have a friend with tools and nimbler fingers than mine. He's not familiar with Mac's. 

This is model iMac14,1 late 2013.

My problem is: How to get a functioning OS on the new drive so I can clone my old drive onto it.

I CANNOT install the latest Mac OS. If I do (I think) I won't be able to clone my current OS (High Sierra) backwards over it. Most of my important apps and games aren't compatible after High Sierra. 

There's a 20$$ Mountain Lion OS in the Apple mac store, but I don't for sure know how to install it on the iMac - the Mountain Lion OS is a download. Do I have to borrow a dvd player and burn a disk, and use the dvd player for an install - or is it good enough to have the dmg on my current peripheral drive?

Will this even work?  1) Have a OS ready on the new internal drive, 2) clone (Carbon Copy Cloner) my current working OS - I'm booting into it on a peripheral drive - over the new OS on the new drive. 

I know - so many questions. If you have advice, I'm grateful.
clone (Carbon Copy Cloner) my current working OS - I'm booting into it on a peripheral drive

I understand you are running off of an external drive now.  

The iMacs are rather tedious to disassemble and re-assemble. They're like laptops.  Your friend should have experience working with pc laptops. Have him look over the instructions and see if it is within his skill set. 

You may want to continue this way.  I'd recommend a second drive as a backup.  I would get an external ssd drive and use the current drive as backup. Give OWC a call 1.800.275.4576.  They will be able to advise you on which external drive for you machine will give you the best performance. I'm running an SSD off of an external drive. Performance is much improved over my rotating internal drive.  At first, I tried my usb 2.0 external drive.  It was too slow.  So I switch to a USB 3.0 external drive which gives me great performance. 

One thing you missed is that you do not need an operating system on you new drive before using ccc to clone to a new drive. 

I'm an elderly woman who is partially blind. I did find a step by step guide on iFixit and have a friend with tools and nimbler fingers than mine. He's not familiar with Mac's.

Your question is well written.  Hardware is hardware.

This is model iMac14,1 late 2013.

My problem is: How to get a functioning OS on the new drive so I can clone my old drive onto it.

You cannot be booted from the internal drive while cloning. So, there is no need for a starter macOS on it. 

the plan


replace your internal drive.  I recommend a SSD drive. Costs a little more, but makes a noticeable speed improvement on your mac.
boot from your external drive.
Use CCC to clone your external drive to your internal drive.