Hi jrivera_eizo,
Now, answer your questions:
1. Is the current version of CodeWarrior still compatible with MK10DX256VMC7? If not which IDE should be chosen?
Answer: To be honest, this MK10DX256VMC7 is very old, even the new MCUXpresso IDE can't support it, as no new SDK for it.
So, if you still use the MK10DX256VMC7, you can still use the Codewarrior, although it already don't update the kinetis.
In fact, we recommend the customer use MK22FN128VDC10 to replace your MK10DX256VMC7.
Or, you also can use 3rd part IDE, IAR, MDK.
2.If CodeWarrior is compatible, should we be concerned with the fact that the new MCU isn't listed inside the header? Are there supporting files that exist that allow the MK10DX256VMC7 to still be used?
Answer: About the header, don't worry, you can use it.
That header can support MK10DX256VLL7, MK10DX256VLL7 and the MK10DX256VMC7 are the same reference manual, so you can use it.
3.Are there any other special considerations that should be known if still the "MK10DX256" bareboard template is used despite the MCU not being listed?
Answer: You just need to care about the detail pin function, to the header, I think it's OK.
Or you can change to use MK22FN128VDC10, which already in the MCUXPresso and the SDK support list:
https://mcuxpresso.nxp.com/en/select

Wish it helps you!
Best Regards,
Kerry