Arijeet

Which inverter doesn't show this information. 
 
My hybrid sunsynk inverter shows exactly where power is coming from or going to. 
First pic shows pv generation, loads supplied by the inverter, battery power and grid power. 
Second pic is from their app and the direction changes depending on where power is going or coming from. 

Some do, some are much simpler and just pour everything that they can generate into the AC output (unless that would result in too high a voltage). If your utility doesn't want you exporting power, then the inverter might try to limit its output so that this rarely happens.
You can think of it as conservation of energy/power: with 10 kW going out, and say 5.5 kW from the inverter, then the remaining 4.5 kW has to come from somewhere; this will be from the grid.

Let me try to answer this: A grid tie inverter synchronises it's supply to the mains. So they will be in phase with each other. (So if these are connected to each other then there will be little or no current that will flow between them)
The PV panels are used to power the inverter and this will produce AC voltage which is used to feed the loads in your house. If there isn't enough power from the PV panels the AC supply voltage will drop and there will then be a voltage difference between the grid and the inverter. The inverter control system will detect this and feed power in from the grid to assist the inverter.
Likewise if there is a higher output voltage produced by the inverter from the PV panels this will be detected and the controller will connect this to the grid allowing the power to be fed into the grid.
These grid tie inverters are smart devices, way smarter than a regular off grid solar inverter!