Some of your confusion about the organisation of major events in soccer is caused by truly international nature of soccer and the way it is almost political.First you need to draw a distinction between club competitions and international competitions.
International teams take the name of the country in which they play and players themselves are selected by the manager hired by that countrys soccer administrative bodies.The manager need not be a national of the team he manages
Club teams are usually based within a city or district and often have players of many nationalities playing for them.(Chelsea is notorious for having only two Englishmen playing for them yet they are based in London)
The top club teams have players who are so good that they also have been selected to reprsent their nation.
The players qualify for selection of a national team based on their ancestry but this can be confusing because there have been notorious cases where the selected palyer has say an Irish Aunt or whatever but has never set foot in that country, it’s a rule that is creatively interpreted.
Once a player has been selected and has played for a particular national team though they generally cannot change, though means do exist such as taking citizenship of the selcting nation and on being resident there for a certain period.
FIFA - Is the body that organises the majority of world international matches and all the important international tournaments.
FIFA has divided the world up into regions and runs competitions within those regions, the two most important are Europe, and South America.These regional competitions culminate in a regional series of finals every four years.
The teams are organised in mini-leagues, I will not go into the way these mini-groups are determined as it may get too complex and boring.
Suffice to say,
Every national team is rated by FIFA according to a complex and sometimes arbitary system of rules according to their results. It is a distinct advantage to be classed as one of the higher rated teams as it means you don’t get to meet other favourites in the early stages of the tournament.
FIFA also runs the world cup soccer tournament every 4 years, in between the regional competitions, and their playoff system is similar to the regional competitions.
Ok now on to the regions themselves.
Each region has its own governing body, in Europe it is EUFA which promotes the interests of its member nations and clubs to FIFA.
EUFA is in fact a very powerful organistion since it is based in soccers ‘centre of gravity’ and as such can and does force changes in FIFA policy.
EUFA organises some regional international matches but is more responsible for organising international club fixtures.
These are competitions that pit the top European soccer clubs against each other, but to qualify for these competitions a club must either win their own domestic trophies or be placed in the top two or three in thier own domestic leagues.
Taking a step down from regional level we have National domestic Leagues.
To many soccer supporters the domestic leagues and cup competitionas are far more important than the regional and world championships.
In England there is more than one body organising soccer but there is little overlap and their competitions complement each other nicely.
I think I’ll leave it there for a while but you can see why there apears to be so many tournaments, there are anomolies but in general what you have is a heirarchy of soccer.
World Cup internationals.FIFA
Regional Internationals.FIFA and EUFA
Regional Club Internationals.EUFA, African Nations, etc
National League and cup competition. English(or whatever nationality) Football Association(EFA)
I think that it would be wise to leave out the organisation of amateur soccer which seems to vary at times as often as the British weather.