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Yes, you can configure different forms to upload to different folders.

This code example:

<?php
add_filter("gform_upload_path", "change_upload_path", 20, 2);
function change_upload_path($path_info, $form_id){
$path_info["path"] = "/new/path/";
$path_info["url"] = "http://new_url.com/images/";
return $path_info;
}
?>

Would apply that change to ALL forms. Note you have to use the correct absolute path to the folder, you may have to work with your web host if you are unsure what that should be.

If you want to apply this to a specific form you would use (in this example form id 5 only):

<?php
add_filter("gform_upload_path_5", "change_upload_path", 20, 2);
function change_upload_path($path_info, $form_id){
$path_info["path"] = "/new/path/";
$path_info["url"] = "http://new_url.com/images/";
return $path_info;
}
?>

Notice the difference in the add_filter call, the form is appended to the end and it is form id 5.

gform_upload_path applies it to all forms.

gform_upload_path_5 applies it just to form id 5. So you'd change _5 to whatever the form id is.

This custom code would go in your themes functions.php file, however you have to make sure the absolute path is correct and that it is writeable for it to work.

One of the field options on the File Upload field is allowable file extensions. So you would limit the filetypes by their extension (ex. .jpg, .gif, .zip, etc.).

It doesn't matter if it's accessible to the public as long as it's accessible to the PHP executing on your site. Keep in mind if it's not accessible to the public then how will you view/access it other than via directly accessing the file system? The URL in the code above is so it can create a URL to use to link to the file from the entry detail page, notification emails, etc.

If you don't want them to access it, don't use a URL that is accessible then or use one that requires you to enter a server username/password to access by password protecting it on the server.