I was wondering, since I just finished my first homework piece: do I need a new pseudonym for every piece I write?
For example, if, for my first charms piece I was "Sarah Clarkson", could I also use "Sarah Clarkson" for my second charms assignment, or would I have to use a different one?

Yes, please use a new homework pseudonym. Oftentimes we help out each other with grading so we will notice if pseudonyms are consistent. 

The same can be said about formatting. If you format something similar to an rp post, for example, it can make you identifiable. 

We want to have as little bias on homework as possible, so please do vary your information. Thanks for the question