First of all, it helps to know WHEN an auto-enter calc will evaluate (what triggers it).
I would recommend watching this devcon session:
But, the quick answer is that an auto-enter calc will normally evaluate when it is created, or when one of the fields referenced in the calculation is modified.
The beauty of auto-enter calc fields is that you can set them up to automatically enter a calculated result (as the name implies), but then the user can over-ride that result if they want - something they can't do with a plain calculation field.
That said, on to your questions...
Do not replace existing value (if any)
If this is checked, the field will only evaluate if it is blank. Once it has a value, the only way it can change is by user intervention. This is handy if you want the user to have the final say. But remember that if they alter one of the fields referenced in the calc, the auto-enter field will not update.
Prohibit modification of value during data entry
This means that the user is not allowed to alter/modify/over-ride the contents of the field. Checking this makes it more like a regular calculated field… but still not the same, depending on your indexing options. Watch that DevCon video linked above for all of the minutia of what makes a field evaluate. It can seem kinda dry, but knowing this stuff will save you tons of headache when you are trying to figure out why a field will or will not update.
Hope that helps!
Thank you, I'll watch the session.