Can I migrate El Capitan from an external hard drive to new M1 iMac?

There are a couple of questions here. First, your M1 Mac will only run with the OS it came with and then with later upgrades. No Mac can operate with any OS which is older than the one it came with regardless of whether it's installed on the HD or on an external disk. Second, Migration Assistant is an app Apple provides specifically for transferring our data from an older computer to a new one. Use it for that. It will provide options to transfer your personal preferences and settings, your apps and your files. For each group, you can transfer all or none, as you select. It will not transfer your operating system or erase anything from the old Mac. Migration Assistant identifies any disk (internal or external) which has an OS on it and then can transfer either to or from it. Most importantly, use only a USB cable to connect the two computers. Wi-Fi is simply too slow and often fails. Carbon Copy, while being an excellent app is designed for backing up and restoration primarily. (I also use it.) Enjoy your new Mac.

Q - " Yes, it has the M1 chip. I believe the majority of my apps are 64bit. "

A - Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Q - " Apple doesn't say on their sales pages which OS comes with the iMac and I assume it is the latest "

A - The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there. With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. 

Q - " Apple does not offer a USB-C to Thunderbolt 3 or 4 connection and may have to rely on WiFi for the transfer. "

A - Move your content to a new Mac

You have posed a number of questions. Here is some information which should be helpful. Migration Assistant is very easy to use. Be sure to read and follow its instructions as you progress. Basically, the process is as follows.

You first begin by starting the process of setting up your new computer. You will be asked if you wish to transfer files. Respond YES and follow the instructions you will be given.

You will be told to turn both computers on and activate Migration Assistant in the old computer.

The computers should be connected with a USB cable to facilitate the transfer.  (As I said Wi-Fi is simply not suited for a transfer of so much data and corruption often results.)

You will be given several options as to what to transfer. You will likely want to transfer your settings and preferences.

You can transfer all or none of your files or apps. You do not have an option to select certain files or apps to transfer. If you wish to do that, then do so manually. Some people prefer to download and install new apps in the new computer. In either case, you may have to reregister or upgrade some older apps. Note that if you are running any old 32 bit apps in the old Mac, they will not function in the new Mac and 64 bit versions will have to be newly installed there. And there can be a cost for the upgrade in some cases.

The old computer's operating system will not be transferred. No data from the old computer is erased.

Allow for up to an hour for the transfer process to complete once you start it.

It should set up the new computer the same as the old one.

As to the cable you need, get one with the right connecters on each end that match the USB ports on each computer. If you check Apple's support sales site, it has some excellent pictures to show you what is needed. You ask about the wireless keyboard cable. My answer is does the cable have the right connecters that you need? It's a simple matter to look at it and see. In the alternative an Ethernet cable will work, but it will be slower.

When completed you will have two user accounts in the computer. You may either delete one of them or select one to use.

Just follow the instructions and everything should go just fine.

If the new computer is going to be the Apple Silicon M1 Equipped Computer - would suggest Only Migrating the User Account and nothing more.

1 - Apple Silicon with either Big Sur macOS 11 or Monterey macOS 12 Only Support everything 64 bit and there is no workaround.

2 - Issues that may exist on the older computer will be migrated to the New Computer. This would badly pollute the new Original and Pristine installation of the new OS.

3 -  Applications, extensions and Software Drivers may or may not even work on the new computer.

4 - IMHO - it would be best to only install new application etc Directly from the Developer or the Apple Apps Store.

5 - Due Diligence on New Applications and make sure they are Monterey / Big Sur compatible and factor in the ARMs CPU of the Apple Silicon Computer  

Ok and good luck in the endeavour.