Is the sun shrinking currently? The Sun loses about 5.5 million tonnes of mass every second, does this mean Sun's volume is also going down? If so can we tell by how much every year?
E:
&quot;by how much&quot; I mean can we tell if sun's radius is going down too
Is the sun shrinking currently?

It's the other way around: The Sun is slowly growing hotter and thus is slowly expanding. The Sun accumulates ever more helium in its core as it ages. This growing amount of fusion ash results in the core getting hotter, which in turn results in the Sun expanding in volume. This completely overwhelms what one would expect from looking only at the mass loss due to fusion and solar winds.
The solar mass loss rate currently is on the order of $10^{-13}$ solar masses per year. At that rate, it would take on the order of ten trillion years for the Sun to consume or expel all of its mass. That's a much longer time span than the Sun's much faster aging process. The Sun has five to seven billion years or so left on the main sequence. Shortly before the time the Sun leaves the main sequence, it will be about twice as luminous and considerably larger than it is now. Shortly after the the Sun leaves the main sequence, it will be much more luminous and even larger than it was just before it left the main sequence.