Electronic – Transistor Common Base configuration

I thought the collector-base junction was reverse biased which means that the electric field created by the external bias adds to the potential barrier? How is it that holes spontaneously cross this huge potential barrier?

The built-in potential stops the diffusion current due to majority carriers diffusing from one side to the other. For example, electrons in the N material would diffuse to the P material (where they would recombine) if it weren't for the built-in potential. For the majority carriers, the built-potential is a barrier.

But in the N material of the base, holes are minority carriers and so, the built-in potential isn't a barrier at all. If a hole in the base exists long enough, it may be swept across the reverse biased base-collector junction by the electric field there and into the collector region.

When the base-emitter junction is 'on', lots of holes are injected into the thin and lightly doped base region so a large fraction of the injected holes exist long enough to 'slide down' the potential and into the collector region where they are majority carriers.

I am having trouble understanding the three operation modes of a transistor.

When we talk about the modes of operation of a transistor, we're usually talking about cut-off, forward-active, and saturated operation.

The rest of your question seems to be about the different fundamental amplifier configurations, rather than the operating modes, so that's what I'll answer about.

Consider the CE mode. The collector and Emitter both are negative (for npn)

Check your diagrams again. For an NPN CE stage, the base and collector are both biased at higher potential than the emitter.

then how can we reverse bias them?

For a CE stage, the base-emitter junction should be forward biased; the base-collector junction is reverse biased. This is achieved by biasing the collector at a higher potential than the base. This is exactly what's shown in the diagram you posted.

Why is the common pin (the base , the emitter , and the collector respectively) grounded? what is the significance of grounding them?

They aren't necessarily grounded. They are connected to some potential that is equivalent to ground in the ac equivalent circuit. Particularly for common-base stages or PNP common-emitter stages, this is usually not the same as the circuit ground.

The significance is that this node is "common". A node that is used in common between the other nodes to define their potentials. The fact that the emitter is connected to the common node is why we call a common-emitter stage a common emitter stage.

How does a CE mode amplify more than a CB mode ?

A common emitter stage has voltage and current gain. A common base stage is essentially a unity gain current buffer. You need to study the common emitter stage to understand why it has voltage and current gain, and study the common base stage to understand why it is a unity gain buffer. Once you understand those two things, you'll understand why the one stage has more gain than the other.