Is it possible to set it so that after placing an order, customers can login to their account at a later date and check their order status? I have login box but when customer logs in at the moment there is no 'My Account' for example.
Yes. That's exactly what we have on this website. When you login you have a link 'Your account->Your orders' which displays a listing of your orders.
You just have to create a joomla menu via the menu manager manager of type HikaShop user control panel and limit it to registered users.
