The eBay app is great for keeping up to date with everything. You can download it for free from which ever app store you use for your phone. When you download it and login, scroll down the bottom to find the settings. In there is notifications. You can set which notifications you want to receive and which sound you want for each one.
If a buyer sends a message via eBay messages, you will be notified of the message and you can reply straight away if you're able to. You will also be notified if bids are placed on an auction listing and also when an item sells. You can also set it to let you know when a buyer pays.
There are a few restrictions on the app, like you can't send invoices, but if you need to send one from your phone, just go to the desktop version via the browser in your phone.
