While you're weighing the rods as they go in and come out, don't forget about transmutation to volatile elements like Radon, loss of Neutrons, and high-energy fission particles recoiling out of the rods entirely.

A dumb mass-in vs mass-out and E=MC^2 is GIGO, IMHO.

Also, please learn to round numbers to useful values. 8 or 12 digit numbers demonstrate your unfamiliarity with scientific notation, as well as its philosophy.

Go and do your own homework, then return when you have meaningful answers. In particular, imagine that your question (3) is a null hypothesis. If you reverse this question, what does it imply?

(and for comparison with your Q2, the Sun loses 4.3 million tonnes of mass per second - although this is by fusion, not fission, but it gives you some context for the energetics of the solar system)

To help you with your homework:-

The sun produces 3.9 e26 watts by transmutation of 4.3 e9 kg of mass per second.

The Earth intercepts sunshine equivalent to 1350 W/m^2. Integrated over the disc of the Earth, this is 1.72 e14 Watts (i.e. a fraction of 4.41 e-10 of all the Sun's output)

This equates to a mass equivalent of 1.9 kg per second, 24 hrs per day, 365 days per year.

That's 164 tonnes per day; 60,000 tonnes per year.

Compared to that, our entire inventory of nuclear weapons and the fuel for every nuclear reactor on Earth is a mere candle.

Now, bugger off and get an education...