Hi Alex. My Name is XXXXX XXXXX I look forward to assisting you today with your question.
Is there a way to install an old application like Eudora 6.2.4 on OSX Mountain Lion now that Apple removed the Rosetta support?
Unfortunately, No. There is no way to install Rosetta applications on Mountaion Lion
If it's not possible, is there a way to import all the messages sent in over 10 years (in/out/other folders) and the attachments from Eudora 6.2.4 to another email client?
Yes, that is possible. But there will be some formatting and compatability issues like you listed in your question.
Another option could be to install an older version of OSX on the new MacBook, is that possible? Now it runs OSX Mountain Lion, we know that Eudora can work on OSX Snow Leopard.
No. It is not possible. Because the oldest version of Mac OS X that you can run is the version that came with your Mac. Your Mac came with 10.8 Mountain Lion. Snow Leopard doesn't have the requires hardware files i.e kexts files needed for the new chipsets or hardware that come in the new macs. You will not be able to boot your Mac to Snow Leopard even if you install it.
It is not free, but try the trial version before buying it. You can use it to convert your Eudora mailboxes to new Apple Mail format.
Try Emailchemy and please let me know the results.