When an order comes in an invoice is created automatically and gets send out. I can also find that invoice when i click on the order. If I ship the order then, the shipment email goes out to the costumer but the process is still on processing in the order overview but not in the order itself. If i go on shipments then there is also no shipment shown. The same problem comes up with a credit memo.
Data in grid comes from separate table
sales_order_grid. The magento updates this table by cron. Please check that your cron properly configured and run.
Also maybe this one topic will be in interest Rebuilding sales_order_grid