How would synapses behave if resting potential was zero? Assuming that the resting potential is zero and the other mechanisms were exactly the same, how would it affect the generation of spikes in terms of excitatory and inhibitory postsynaptic potentials(EPSP and IPSP). Trying to understand the reason behind negative resting potential, not how it is maintained, but why so. Does it mean EPSP is inherently suppressed by design?
There are two very different questions here. The first question is simple (although it could be interpreted a few different ways). The second question is very tricky and I am actually not certain we know the answer.

1. What do PSPs look like if the resting membrane potential is 0 mV?

If a cell is being held at 0 mV, its voltage-gated conductances are essentially broken and it is not actually able to fire an action potential. But let's put that aside and focus on synaptic events. Let's also assume that the reversal potentials for each ion are 'normal'. 

The short story is that most excitatory receptors have a reversal potential near 0 mV, so EPSPs would have little direct effect on the membrane potential (remember this rule: current passing through an ion channel can only push the membrane potential toward the reversal potential of that channel). Inhibitory receptors tend to reverse around -75 mV, so they would have a large driving force and would strongly polarize the cell. 

The slightly-longer story is that EPSPS would still have some effect--when ion channels open, ions flow in the direction of their electrochemical gradient. For excitatory receptors, this means that sodium flows into the cell, potassium flows out, and calcium flows in. The net electrical current would be roughly zero, but there would be an exchange of ions, and an opportunity for those ions to activate secondary signaling pathways. 

Another effect of opening ion channels is a reduction in the resistance of the cell membrane. Thus at 0 mV, excitatory synapses can actually shunt IPSPs.

2. What is the reason for having a negative resting potential at all?

The first thing to recognize is that neurons store a large amount of energy in their chemical gradients. Potassium is pumped into the cell while sodium, chloride, and calcium are pumped out. Running these pumps is metabolically expensive (your brain takes up 20% of your metabolism at rest!), and the chemical energy burned in the process (ATP) becomes potential energy in the chemical gradient. Another way of saying this is that each of these ions prefers to be on the other side of the membrane, but the pumps keep them where they are. 

Ions are generally pumped in such a way as to maintain charge balance--for every positive charge pumped in, one positive charge goes out. Now if you happen to have channels that admit only a single type of ion (we do), then opening that channel will result in an immediate flow of ions. But wait! Unlike the pumps, this ion flow is not charge-neutral, so after a very short time, the membrane becomes charged, and that charge imbalance (voltage) counteracts the chemical gradient (if ions dislike being on the wrong side of a chemical gradient, they absolutely hate being on the wrong side of an electrical gradient). 

So what we have now is a huge energy store in the form of chemical gradients, and a means for the neuron to rapidly convert that energy into electrical potential. If the neuron wants to depolarize, it needs only open sodium or calcium channels. If it wants to repolarize, it opens potassium or chloride channels. You can think of it like a balloon connected by hose to two tanks: one high pressure, the other a vacuum. Open one valve and the balloon fills, open the other and it empties. 

Ok, that was long but I am finally ready to talk about resting potential. The how is easy: neuronal membranes are more permeable to potassium than sodium. One of the valves is always open a little bit, and this drags the membrane potential negative, away from zero. Which is to say that the resting membrane potential is not at all the "driving force" for neuronal activity. Rather, it is almost just a side-effect of the real powerhouse--the chemical gradients.

I mentioned that neurons spend a lot of energy maintaining their chemical gradients. Why then, would the cell allow its potassium gradient to simply leak away? This is not an easy question! The lazy answer is "because all the voltage-sensitive channels operate in the range from -70 to 0 mV". I call this lazy because if there really was no benefit to having the cell rest at -70 mV, then evolution would find a way to conserve all that energy wasted by leaking potassium. So there must be a better reason. I've turned this into its own question here: Why do neurons have a negative resting potential?