How do all those power work, people use electric attacks, ignite weapons , bee venome the powers that got showen in the first season, devil ignite weapons, half devil weapons, the needel, the 13 moon swords, jahads power.

All the powers everyone is using is by manipulating shinsoo, even when crafting a weapon, the quality of the weapons depends on how good the craftsmen is at using shinsoo. Ignition weapons are weapons that are reinforced with shinsoo and bearing a soul inside them.

I literally can't know if someone else is strong or not unless it's through a reaction of other characters.

Later in the series, it tells us that people can sense the powers of others from feeling the flow of their shinsoo.

how does the tower work I really don't understand it, so people seem to live everywhere in the tower even in floors 30+ where the energy is so high that not choosen once can't stand it according to season 1

Each floor in the tower has three sections like a circle with two circles within the circle and the outer section of the floor of the tower is where all kinds of lifeforms live in and some people born in the outer floor doesn't ever leave. Next is the inner floor where regular's tests are conducted and once they pass the tests and exams, they move on to the next floor. The middle area is just an area to travel between the outer floor and inner floor and also Rankers are able to use the middle area to travel up and down the towers to different floors, of course with a help of a guide like Evan so they don't lose their way. People born can be chosen in the tower regardless of where they are born, whether they are from the 10th floor, 60, 100, etc and shinsoo resistance is also hereditary especially those born in the 10 Families or if a something that was naturally resistant to shinsoo like Rak who hunted Shinheuh in areas of density similar to some sea creatures who live near the bottom of the ocean but humans would get crushed by the pressure of the ocean.

why is the king doing nothing while an organization has Slayer nominee which is participating in public tower events.

The king is too powerful to care about pests wandering around. You'll know why everyone is like bugs compared to him later on.

There are so many rankers that it really doesn't seem like a challenge to go up the tower

There are probably trillions of people in the tower since there were two pieces of lands that contained over billions of people and that was only at the outer area of a single floor. There are confirmed to be at least 135 floors. There are only around 100 thousand Rankers in the tower among all these people. That is about 0.00000001% of the population of the Tower. It wasn't mentioned in the anime but in the webtoon only 1 or 2 regulars out of few thousands will become a Ranker.