Hi Athena,
Your solution may be a bit premature...
Without living in the home for at least a period of time both dry and wet weather...how to plane the basement would be ill advised. I have seen many that have a sump pump down in them because they don't have good drainage (or blocked drainage) on the outside. There are other reasons too. Many dirt floor basements are 'bone dry' and need no further augmentation from the original form other that shelves and bins to make them "back into root cellars" which many had been.
If you want to add white wash lime paint for brightening and esthetics...that is fine. I like the looks of stone, timber and brick in their natural state...but have added "white features" to the area to brighten things up a bit...as well as other colors...
Critters be what they are...rodent proofing a floor may not be
enough...
Are you living there yet?
If not...when?
I will follow along and help wherever I may.
Regards,
j