Learn Finnish: Voit hieroa lamppua milloin tahansa.

Tahansa is added directly after a question word to create a "free-choice" phrase, similar to adding "-ever" or "any-" in English. Since milloin means "when," combining it with tahansa translates to "whenever" or "anytime."

Is the word order fixed, or could I say tahansa milloin?

The word order is strictly fixed. The question word (such as milloin, kuka, or mikä) must always come before tahansa.

Could I use koska tahansa instead of milloin tahansa here?

Yes! Both milloin tahansa and koska tahansa are very common ways to say "anytime" or "whenever." They are completely interchangeable in this context.

Why is the object lamppua in the partitive case?

The verb hieroa (to rub) typically takes a partitive object because it expresses an ongoing or incomplete action. You aren't "finishing" or "consuming" the lamp by rubbing it, so it takes the partitive form lamppua rather than the total object form lampun.