Yes, you can use the app simultaneously on multiple devices. You don't have to log out in order to login on a different device, so feel free to download the app and use it on multiple devices, for example a phone and a tablet to use at any time, wherever you are.
Your survey answers, checklists and exercises logged on the app will sync between your different devices. Note that any exercise videos that you have added yourself can only be watched on the device where they were created.
Note: Syncing of data happens only when an activity is completed - so don't be surprised if you need to use the app for a while on a device, before data is completely synced from your other devices.