If by '... I'm not a PHP developer...' you mean you don't write any code, then my suggestions might not be helpful. I apologize in advance if that's the case. I don't believe you'll be able to accomplish what you want without getting your hands a little dirty in some code ;)

Attach the fields you need from a customer to the commerce_order bundle. Can do this in hook_install(), using field_create_field() and field_create_instance(). I prefer to create the fields in the UI and use Field Inspector (http://drupal.org/project/field_inspector) or Features (http://drupal.org/project/features) to export the field config and instance arrays since they can be pretty big. You can create them on a test content type and just remember to change the 'bundle', and 'entity_type' properties to 'commerce_order'. The order edit page uses field_attach_form() so adding these fields to the commerce_order bundle should have them automatically added to the order edit form.

You can then use hook_commerce_checkout_pane_info() and field_attach_form() to place the desired fields (from your updated commerce_order bundle) as form elements in a checkout page. You can always just unset() fields you don't want before returning the form array.

So now you have the form in checkout with all the data you'd like to collect from a customer, and you have the means of seeing that data via order edit. I think the tricky part is payment being an asynchronous process. It will depend on your chosen payment gateway, and whether you want to leave the order in a 'Shopping Cart' state and email the user a link to get back there (with the proper permissions, and the gateway enabled), or to send them a link directly to the gateway making sure you've got all the details pre-populated so they don't need to fill in their info again. Either way you're looking at creating some Rules that fire on event 'After updating an existing commerce order' and have a condition be that order status is 'Complete' or some custom status you want it to be to mark that the order can move forward to payment (use hook_commerce_order_status_info()).