TC internal drive needs repair

From your questions we are going about this the wrong way.

You need hands on help.. not remote forums from people in a different country.

Stick to Time Machine.

Buy a new router that is suitable to your setup .. I have already listed a couple. And buy a USB drive to plug into it.

I strongly recommend going to a store that works with Apple or has Mac knowledgeable staff and get them to help you set this up in the store so you can just bring it home and plug it in.

Or get a local tech into your house and let him quote for setting it up for you.

And be upset that Apple has left you stranded. They eliminated the tool you require and provided nothing in its place.

I hope you saw the post current with yours.

You can try doing a one pass erase to see if the disk can be recovered but I would say it is unlikely to be trustworthy again. IF that fails then disk has actually failed badly.

https://discussions.apple.com/thread/251347859

If you have had the TC for a few years and certainly more than 5 years it is time to replace regardless.

My current time capsule is 802.11AC 3TB

How old is it Perry?

Is swapping out the disk something you would be happy with doing? In all honesty I would NOT do it for unit over 5 years.. and I would umm and arghh about over 3years.

You can continue wireless backups but you will need to decide a way forward.

will i have to plug in an external hard drive to my iMac to use time machine

This is far faster and far more reliable method of backup. You can setup the iMac to also backup the Macbook over wifi.

You need to be on High Sierra or later.

https://www.howtogeek.com/330288/how-to-set-up-your-mac-to-act-as-a-networked-time-machine-drive/

I note that Bob... one of the Gurus here tried it and said it wasn't great. However as below Carbon Copy Cloner might work fine. TM is more a problem than sharing the backup disk.

So alternatives are using a 3rd party wireless router which supports time machine to USB3 drive plugged into the router. This is the cheapest alternative.

Synology RT2600AC is excellent.

High end Asus support it but in my experience you should be using Carbon Copy Cloner rather than Time Machine.

Some cheaper routers have started supporting it but I would not be trusting them without lots of testing. Especially if you are on Catalina run CCC or alternative cloner.

A Synology NAS is a very good choice.. and even with Time Machine seems quite reliable. Expensive solution though for just backup although you might find a cheap single or dual disk model Synology second hand.

You will need to remove the disk from the TC or replace it so TC can work as a router but will give you disk errors forevermore.

So it is worth replacing as a router IMHO.

Modern units are far better wifi and routing ability.

Will I have to plug in an external hard drive to my iMac to use time machine = if i buy a 4TB drive can i just unplug from iMac and plug into mac book to back that up and will it keep both back ups separate?

I would partition the external drive.. so if you buy 4TB which is a good size..

IMHO don't buy 2.5" type above 2TB as they use SMR format and very slow.. see more below.

Get desktop drive which have 3.5" drives in them.. partition into two parts and you can backup one Mac to first partition and one Mac to the second partition. That keeps the two Macs entirely separate.

Would it be best to get 2 X 2TB external drives one-for each mac?

I do like keeping the drive connected.. and 2TB you can buy portable drive.. so in the iMac it will be invisible and powered over USB.. easy. It also means the if one drive fails you still have one backup whereas the one backup drive fails and you have lost all the backups.

In a way it depends on how you use the Macbook. Personally I prefer to do network backups on them over wireless just for automatic backup without user intervention it works better. I don't like plugging and unplugging something every day..

If your Macbook is running to a dock though, you can plug in one connection and that makes it easy.

How does CCC work, I presume you download it on each mac and store the CCC on a hard drive somehow?

CCC is an application.. you download and install it.

Do i need to purchase for each mac?

Is it a yearly cost or a one off cost?

One license is permanent (only need to upgrade license for new version.. patches are free for current version) and you can use on as many computer in your home as you have on one license so it is pretty reasonable.

There are alternatives which are also popular.. superduper being one well known and popular.

I find CCC more functional and better support.

Download it for free and use it for a month free without any limitations. That gives you a chance to learn how to use it and decide for yourself.

My setup is CCC once a day to USB drive. This is bootable clone so I can check the backup every now and then by booting the computer from it. I do still run Time Machine to help people with questions but I trust it not at all.

It regularly wipes itself out. After several years of this I wised up. CCC has never let me down.

I do run Time Machine to several targets.. a second partition on the same external drive as CCC bootable clone.. that is the best for TM. I run it to a Time Capsule.. for old times sake.. and a Synology NAS which is also very good.

CCC is different and you can follow the setup tutorial.

https://bombich.com/kb/ccc5/how-set-up-your-first-backup

There are also youtube tutorials. You won't find it hard.. interface is very clean and best of all the logs.. just click on task history on the main screen and you can see the list of backups.

If you are going to backup Catalina.. there is some important info to note.

If your backup disk is a "mobile" 2.5" rotational disk (i.e. that spins at 5400RPM or less), we recommend that you format that device as "Mac OS Extended, Journaled" (aka HFS+) and use it for data-only backups. APFS offers unacceptable performance on these devices, we simply can't recommend nor support the use of these devices for bootable backups.

https://bombich.com/kb/ccc5/frequently-asked-questions-about-ccc-and-macos-catalina

https://bombich.com/blog/2019/09/12/analysis-apfs-enumeration-performance-on-rotational-hard-drives

CCC has extensive and excellent KB articles and support if you ever need it.

NOTE I have no affiliation to them and pay for a license same as any other user.