Do I report it as income? Is it subject to just the same amount of
taxes (~30%) as regular income? Are there any restrictions on how it
can be used?
It is income. You can deduct the costs of maintaining the web page and producing the software from it (have an accountant do that for you, there are strict rules on how to do that, and you can only deduct up to the income if its a hobby and not a for-profit business), but otherwise it's earned income like any other self employment income. It is reported on your schedule C or on line 21 of your 1040 (miscellaneous income), and you're also liable for self-employment taxes on this income.
There are no restrictions, it's your money.
Technically, who is the donation even being made to? Me, just because
I own the webpage?
This is for the United States, but is there any difference if the
donations come from overseas?
No, unless you paid foreign taxes on the money (in which case you should fill form 1116 and ask for credit).
If you create an official 501(c) organization to which the donations are given, instead of you getting it directly, the tax treatment will be different. But of course, you have to have a real charitable organization for that.
To avoid confusion - I'm not a licensed tax professional and this is not a tax advice. If in doubt - talk to a EA/CPA licensed in your State.