How to customize keyboard layout / character mappings?

How can I create a custom keyboard layout?

Would like to change the mapping of the keys on my physical keyboard to different characters.  An updated on-screen keyboard would be nice, but is not necessary.

Can the customization be saved and reloaded on another PC?

Any limitations on version of Windows?

Can it be achieved without 3rd party software?

I prefer to use Microsoft software whenever possible in attempts to keep things running smoothly.

Thanks!

More details:

Being able to map my most frequently used keys would significantly decrease the time it takes for me -and my teammates- to complete our work transcribing historic texts; modern keyboards don't exactly align with the writing and punctuation styles used 300+ years ago!

Alternatively, is there a way to request a special layout be added by Microsoft?  A long shot, for sure, but there have been dozens of ultra-specific layouts added since Win10 rollout; I've even come across some "legacy" versions with such minute differences they actually remove characters from the SHIFT mapping!)

Oh, and please, if you suggest submitting a uservoice or similar request, I'd appreciate it if you could be specific about which team I should be directing it to!