Typically the invoice is e-mailed to the client after the transaction is completed. There is currently no facility to show the invoice in the browser at that time, although you can enter a URL to redirect to on completion of an order, so you could set that the 'My Invoices' page if you want (but that might not be much use if the client is not logged in).
For the PDF generator, make sure the /cache/ and /out/ folders are both writable by the user PHP runs under. If it still is not working, try re-downloading the pdfwriter script, and re-uploading it to your site in case any files got corrupted.