1. What documentation do I / might I need to show, stating that I actually used my hardship withdrawal to pay my tuition, after I receive my withdrawal? I've found plenty of information for other withdrawal types - but not this. A copy of the tuition bill or a letter from the registrar. You will need to ask your plan administrator what they will find acceptable.
2. Can I still receive a hardship withdrawal, even though I have student loans and a small grant helping pay my tuition? That is a question for you to ask your plan administrator. However, unless you are in your last year, taking a 401k withdrawal can reduce future financial aid. That's something you'll want to consider as well.
3. Can hardship withdrawals be used for other expenses besides tuition, eviction, funeral expenses or medical expenses? Absolutely not. The IRS only allows hardship withdrawals for six reasons; you've listed four, the others are the purchase of your primary home and in SOME cases, repairs to your primary home. There are no other reasons whatsoever and you will need to provide documentary proof for each one. You also cannot take out more than the amount needed to pay the bill in question, grossed up for taxes if desired.
3a. Is this legal? Is what legal?
You don't mention if you've investigated a loan rather than a hardship withdrawal. Some employers (mine is one of them) will not permit you to take a hardship withdrawal if you have a 401(k) loan option availab.e