Is it possible to display captured values after the form is submitted?

I have a prayer request form, but I wanted to know if the requests can be displayed on the screen below the form once it is submitted

Yes, it's possible by creating a custom thank you message for your form.

You can modify the message and show the values of the submitted fields in it.

You can see a working demo here: http://form.jotformpro.com/form/50137425076956 feel free to clone it to your account if you want to.

Let us know if you need further assistance.
Thanks.

This is great.

is it possible for other users to see the request of others right under the form?

what I meant originally was to have the user submit and see its own request below the form, without going to another page

That's possible too.

You can create a table report or a grid report for your form and embed it in your website. This will allow you to show a list of the prayers that have been previously submitted in your form.

Another option could be to use the Preview Before Submit widget. This widget allows your users to preview what they've entered in your form before submitting it.

Hope this helps.