Sorry to put a lid on your dreams, but:
So I am quite sure that one day I will hit Challenger.
http://www.leagueofgraphs.com/rankings/rank-distribution
0.02% of players are in challenger ELO. That's 1 in 5000 players.
Getting to that point requires more than just "improving". You simply have to be able to do it to begin with. Some people naturally have bette rreaction times, hand-eye-coordination, insight into the game, whatever, than others. If you don't have it in you, you won't get there.
But also im planning to have League of Legends as my full time job
You and millions of others.
Just like tens of millions of people every year decide that they want to be rich and famous pop musicians, actors or models, or social media superstars.
How many of them make it? And how many of them fail?
Aim for a realistic job. Have a safety net. If you find that you are "the one" you can still pursue your dream. But focusing time and effort on something that is dependent on so many factors outside of your control, is just not clever.
Anyways back to the topic, once I hit Challenger how do I join a professional team? Where do I apply?
You don't.
There is no "application form". These teams are not companies hiring people who sent in their CV. Players are noticed and contacted.
And just to put that lid down a bit further..."hitting challenger" is not the prerequisite. Even though its just 0.02%, there are still thousands of challenger players, all competing against each other. Most of these people are years worth of experience ahead of you by the time you get there, if you get there.
Do you think you can just "gradually improve" past all of them? If you are perfectly honest with yourself, do you think there is a reason why this will happen?
And among this elite, only the top teams can participate in the challenger series. To enter the next tier you have to WIN in the challenger series. there is no gradual improvement there, its a tournament.
And even winning in the challenger series is not gonna put you on the top teams (aka. the guys who can make a living of it) either. It gets them a ticket into the LCS, where most challenger series winning teams turn out to be a disappointment and vanish as quickly as they appeared.
Also, just to be clear about something: ^^^^ THAT'S a long post. :-D