When using paypal is there a way to leave the dollar amount empty so that the person who fills out the form enter their own dollar amount?

Yes, you can use user defined payment type:

You can set it in the Payment integration wizard. 

That way your users will have to enter the amount in the payment field.

Let us know if that could work for you.

Thank you!

Can you have more than one product with a user defined amount on a form?
...

Yes, you can. Please check the below.

You could use Input table and form calculations field:

Then you can add products to Form calculations widget (you can make the widget hidden):

And pass it to payment:

So whatever your users enter in products section it will be calculated in calculations field and passed to payment.

This can be done with radio buttons where you set certain numbers and then reveal the text fields accordingly. Then calculate those similarly like above. You can check this guide as well: https://www.jotform.com/help/275-How-to-Pass-a-Calculation-to-a-Payment-Field

Also here is my test form: https://form.jotformpro.com/72426657685974

Let us know if you have any further questions.

Thank you!