Question: How can increasing the radius of earth may cause an impact on the solar system ? Like, would earth may start making a bigger orbit (due to increase in size and wait) or vice versa ? or else ?

PS: The base of my question arises from the point of view of "Growing Population", and managing it by "artificially increasing the size of earth" (Instead of say, finding possibilities to live on other planets like Mars). So, if the radius increases, naturally the circumference of the sphere, and hence surface to live on will increase.

I understand however that probably exploring newer planets might be more feasible solution. But just for curiosity I shared my query. :)

Answer: 
Radius has little to do with an object's orbital properties. Instead, consider its mass.

The mass of a satellite (in this case the Earth) does not affect any properties of its orbit. This makes sense, since the force of gravity is proportional to mass, and acceleration is proportional to force divided by mass. Therefore, the Earth's orbit would not change.

The moon's orbit, however, might. If one were to double the central mass of a body being orbited, the velocity of the orbit would increase by a factor of sqrt(2), causing the period of the moon's orbit to reduce to around 20 days. Also, the moon's orbital radius would decrease, thereby increasing tides slightly.

All and all, there would be few notable changes.
The Earth is getting bigger even now. Although very slowly. There is a constant rain of space dust onto the planet. But it won't make much of a noticeable difference to the planet's size or mass any time soon.

As an engineering effort to make more living space... not very practical. Where would the new mass come from? How could it be safely deposited?

Surface area increases with the square of the radius, volume with the cube of the radius. Let's say you wanted to double the surface area... you'd need to increase the radius by about 1.4 times (square root of 2) i.e. increase it by about 40%, so you'd need to increase the volume by a factor of ((square root of 2) raised to the power of 3) or about 2.8 times. In other words, you'd have to add almost twice the current volume of the Earth just to double it's surface area... like getting 2 Earths for the price of 3.

Let's say we did it anyway... triple the mass of the planet in order to double its surface area. I can't see how it would affect the bulk of the solar system... Earth would still be tiny compared to the Jovian planets and the Sun. It would affect the Moon though... the extra mass would pull it into a closer orbit. But I think that would be about it.