If you take 200 rods of plutonium what would happen due to it’s half-life? If you take 200 rods of plutonium then stick them together would 100 full rods worth of plutonium be remaining? And after half-life #2 here would be 50 rods worth of plutonium left and then after half-life #3 would there be on 25 rods of plutonium rods left and etc.?
 A: The half life doesn't mean that if you start with two rods after the half life one rod has disappeared. After the half life half the plutonium atoms originally present have disappeared, and which atoms disappear is random.
So let's say each rod has $N$ plutonium atoms in it, where we can calculate the number $N$ by dividing the mass of the rod by the mass of a plutonium atom. Then after one half life we still have two rods but now each rod now contains only $N/2$ plutonium atoms and a whole lot of fission products.
In practice the decay of so many of the atoms in the rods would probably make the rods crumble into dust. So after one half life you end up with two piles of dust - each pile containing $N/2$ plutonium atoms. After two half lives each pile would contain $N/4$ plutonium atoms, and so on.
A: Plutonium has several different isotopes, with a wide range of half-lives. So if your rods aren't composed of a single isotope they don't have a well-defined half-life. But if the rods are all composed of a single isotope then they will decay as you describe.
However, if the rods are a fissile isotope (Pu-239 or Pu-241) sticking them together will increase the rate that fission occurs, since the neutrons released by spontaneous fission will have a higher probability of colliding with a Pu nucleus and inducing it to fission. If the bundle of rods is large enough, this chain reaction will rapidly become explosive.
A: If it is plutonium 239, you most probably will have a melt down  the minute you stick them together, because  of the critical mass of plutoniumPu-239

Of all the common nuclear fuels, Pu-239 has the smallest critical mass. A spherical untamped critical mass is about 11 kg (24.2 lbs),3 10.2 cm (4") in diameter.

11kg/200 means each rod should be smaller than 55 grams, so one should make sure of this before "sticking them together". 

Plutonium weighs 19.86 gram per cubic centimeter, 

the critical mass limit says the rods  should be of pencil dimensions. 
For other isotopes  or for Pu239   below the above limit, John's answer applies.
