The animals are easier to answer so I'll do that one first:
There are examples of animals on Earth that have hyper-extended hibernation periods. Take for instance the Periodical Cicada, which hibernates for 13-17 years. They do this in order to stymie potential predators. No natural predator of the cicada ever stayed around because they aren't a stable food source. I won't go into detail as it's complicated to write but fascinating nonetheless.
Anyway, the point is that, if there is a pattern to the Drought/Flood timings then animals could easily adapt to a hibernate/swarm pattern to match - as the drought years approach, aquatic life flocks to the crater to bury eggs in the mud. The mud then dries hard to protect from scavengers.
When the floods return again, the mud softens and the water triggers the hatching of the eggs. Because the animals would have evolved to match the cycle, you wouldn't have cases of tadpoles stuck on the rocks dying because the life cycles of the animals wouldn't lay new eggs until the droughts were coming.
You could have other animals working on the same timescale - it could be that there is little warning of the droughts, so there is a mad scramble to lay the eggs, and some don't make it there in time - these failures or insufficiently buried eggs would become a waking feast for other animals that become dominant in the drought season. This would help keep the aquatic/flood population down as only a small population would start the flood season each time (otherwise there is a risk of overpopulation).
Theoretically this system could occur even if there is no pattern to the drought, provided that there is a slow enough change (some trigger that gives the plant/animal life a small warning) to leave time for the rush upriver. It would also need to be reasonably regular (no random but not uncommon gaps of a decade or so) to be tenable.
This is more difficult because you've specified some details that will be hard to achieve realistically. There is an example of Earth civilisations that have worked with a drought/flood environment — The Egyptians — but they had to cope with a much shorter cycle. Some parallels can be made, but not many. I honestly can't see how an underground society could survive in a periodically flooding area, unless they have a way of sealing their tunnels that doesn't rely on standard physics. The technology that is required to properly seal would never have time to develop - everyone would die/be forced out before the civilisation became that advanced. The question you have to ask yourself is not "How do they keep it out now?" but rather "how did they keep it out before?" There has to be a simple method of keeping out enough water that everyone doesn't drown the first time it happens in order for a society to form at all.
The only way I can think of is if the land around the flood plains is very hilly. The society started in the caves that are high up and remain relatively dry, but as the population grew they had to start trying to waterproof wetter and wetter areas, with the poorest occupying the wettest areas. That way, your waterproofing method doesn't have to be perfect. In fact, it's likely to be made up of things like hastily built dams and constantly dripping sandbag walls, occasionally flooding catastrophically, depending on how much your society cares about the poor.
if you're willing to scrap the underground approach, there are some other societies you might have:
1) No building on the flood plains
The Egyptians dealt with the Nile by not using the flood plains to build on - they used them as farms. All of the actual permanent structures were on land that never actually flooded. Depending on the contours of the land this could be viable - if there is a significant rise in the land limiting the size of the flood plain, then civilisation would naturally form there, if anywhere. During the floods the marshlands could be used as growing areas, like paddy fields. During the droughts... be creative! There could be some special mineral in the water (a by-product of whatever caused that crater, for instance) that can be harvested from the mud during the droughts. This would certainly explain why civilisation formed in such a hard environment in the first place.
2) Nomadic Culture
The culture doesn't deal with the changing landscape because they don't have to. When the landscape starts changing, they up and leave, or even just move to the edge of the flood plain for the duration. None of their buildings are permanent, or the important once are movable (buildings on wheels!). Alternatively, Boats! During the drought season the tribes are scattered across the waterways, with only a small few chosen watchers left behind. As the floods come and a large water-filled basic forms, the tribes all flock back along the waterways to form a central civilisation for the extend of the flood period, sharing advances and discoveries in that time. In theory you could combine the two, or have two nomadic tribes, one water based, one land, that swap control of the same area.
3) Floating Buildings
Every building in this budding metropolis floats on a raft of sort anchored in place by... something of your choice. As the water level rises, the buildings rise with it. As the level falls to nothing, the buildings drop and slowly settle on the drying ground. This drought time allows the people there to tend to the anchors and deal with any decay, potentially replacing any that have rotted through. During flood time sometimes shoddy work comes loose, sending buildings crashing downstream and causing mayhem in the poorer areas of the city.
4) Hybrid Culture
Combine any of the previous 3! Rich people living on hills in a stable environment, poor people having to live on floating rafts in the valleys. The variations are multiple.
5) An Aquatic Civilisation
If we're departing from reality enough that everyone has electric skin, why not make them have gills? Rather than being a land-based society, it's a water-based one. They live underground in water-filled caverns that are filled during the flood season, and slowly dry out during the drought. For them, the problem is the drought season, not the flood, as they struggle to preserve enough water during their flood to last out the dry season.##
There are certain things that any permanent civilisation would have to get a quick handle of. A stable human civilisation requires stable supply of water, so they would have to learn to make reservoirs (big ones) that filled during the floods and would last through the drought. They would have to have a consistent source of food throughout the drought period. Even if it is less bountiful, it would still have to be present. Again, rich people might keep reservoirs/aquariums filled with flood-time delicacies that the poor have to do without.
Finally, just a couple of things that I feel I should point out. First of all, water is attracted to charge, full stop. Water itself is electrically neutral, but this is because it is made up of electrical dipoles - sets of positively and negatively charged particles that cancel each other out. Because of the way water is structured, if you introduce any charge nearby, it will pull the oppositely charged parts towards it, and they pull the whole stream with them in a chain reaction - basically, the static charge unbalances the system in one direction, rather than the water being naturally charged in the first place.
The result of this is that an electrical barrier wouldn't work, but you could still use the concept, by using a giant electrical beacon on the other side of the river to try and bend all the water away from the populated area. That said, it would need to be one MASSIVE charge - one that would potentially electrocute anything in the water, depending on how salty the water is.
Secondly, positively charged skin would be a nightmare due to other properties of physics. Everyone would generate a significant magnetic field, for one. I believe this means that everyone would be repelled by everyone else, something that would make procreation quite difficult! If you want them to not be shocked by electricity, a more convenient approach would be to give their skin the highly insulating properties of rubber. You get shocked because the electricity uses you as a faster conduit to the ground - if your skin is insulating, you won't be chosen as an alternate route when you touch the charged object.
Neither of these things matter if you don't care so much about the accuracy of your physics, just thought they might be worth pointing out! I hope some of that helps.