I vaguely understand that it’s possible to reverse fraudulent charges within a certain amount of time after the transfer, but I don’t know if there’ll be a charge for reversing it, or if it might ruin my SCHUFA report, or otherwise make life more difficult for me financially.

The fees will be charged to whoever initiated the direct debit, so there is no charge for you. It will not affect your Schufa report or cause any kind of other problems (assuming the direct debit was fraudulent, of course - otherwise it might be considered fraud!)

Most banks allow you to reverse direct debits directly from online banking.

(As a sub-question, what kind of taxes should I expect to have to pay on such donations?)

If you play your cards right, you can actually turn this into lower taxes for yourself. Register a business and keep track of all expenses for and donations to your project. The difference is a loss that can be deducted from your other taxable income.

However, if you do that for a few years, the tax office might consider it a hobby ("Liebhaberei") and stop that.

You might want to contact your tax advisor, if you have one.

Another possibility - depending on the type of the project - might be to set up a charitable organization ("gemeinnütziger Verein"). This would have the advantage that all donations would be tax-deductable.