What actions can be taken with lost and locked phone? I lost my phone and I tracked it, but then suddenly I lost the location. Can the person make use of it if it is not screen locked? What other actions can he take with it.
If your missing device is off or offline, you can still put it in Lost Mode, lock it, or remotely erase it. 

The next time your device is online, these actions will take effect. If you remove the device from your account while it's offline, any pending actions for the device will be cancelled.

Once it's in Lost Mode, no-one can do anything with it, it's a brick to all but you, so long as you don't erase it or remove it from Find my iPhone.

Ref: Apple KB - If your iPhone, iPad, or iPod touch is lost or stolen