Let's suppose we have an <input> element where the user can enter a number (e.g. 500).
When clicking some button or so, I want the user to be redirected to the PayPal donation page where they can specify the ammount but to have the default value set to the number set in the input (500 in this case).
Does the PayPal url allows such an option (maybe via querystring parameters)?
Yes it is possible. You will need to create an open source Donation Button in order to have your donors add the donation amount from the form you create rather than on the PayPal Hosted page.
You need to add this to your donation button code
<input type="text" name="amount" size=10><br /><br />
Below is the complete Donation Button Sample code.
<form action="https://www.paypal.com/cgi-bin/webscr" method="post" target="_top">
<input type="hidden" name="cmd" value="_donations">
<!-- Update to Your PayPal Email or Merchant ID -->
<input type="hidden" name="business" value="youremail@email.com">
<input type="hidden" name="lc" value="US">
<!-- Update the Value to the Donation Name -->
<input type="hidden" name="item_name" value="Test Donations"><p>Please Enter an Amount</p>
<!-- The below will allow your customers to enter an amount and this gets passed to PayPal -->
<input type="text" name="amount" size=10><br /><br />
<!-- The rest is the normal PayPal Donation button Info -->
<input type="hidden" name="no_note" value="0">
<input type="hidden" name="cn" value="Add special instructions to the seller:">
<input type="hidden" name="no_shipping" value="2">
<input type="hidden" name="currency_code" value="USD">
<input type="hidden" name="bn" value="PP-DonationsBF:btn_donateCC_LG.gif:NonHosted">
<input type="image" src="https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif" border="0" name="submit" alt="PayPal - The safer, easier way to pay online!">
<img alt="" border="0" src="https://www.paypalobjects.com/en_US/i/scr/pixel.gif" width="1" height="1">
</form>