What are the features of hypermodernism? I know that one feature is controlling the center indirectly (f.ex. fianchetto), and letting the opponent control it with pawns. But I am not sure if there are other features. Nimzowitsch, who was the inventer of the hypermodernism style, wrote several new ideas in his book , such as overprotection, prophylaxis, rook on the seventh rank, knight outposts an so on. Are these ideas also considered as a part of the hypermodern style or is there a clear definition on this?
It seems to me you have the idea spot on already. Traditionally, chess theory was that the best way to control the center was to occupy it. Some players (like Nimzowitsch and others) showed that this was not necessarily true and that there is merit in letting your opponent occupy it while you undermine it from a distance.
I'm not sure if the idea was really novel at the time, but it became popular and as we do whenever we see a pattern we have to name it.
Beyond that I doubt there is much to learn from "hypermodernism" (which is not to say that there is not much to learn from the various rich and deep ideas behind each of the so labelled openings themselves).
Hypermodernism is a school of chess that emerged after World War I. It featured challenges on the chess ideologies presented by central European masters, such as on Wilhelm Steinitz's approach to the centre. It also challenged in particular the dogmatic rules set down by Siegbert Tarrasch. The Hypermoderns challenged the guidelines of the previous generation and demonstrated with concrete games and victories that these challenges could be done successfully. Aron Nimzowitsch for example showed how games could be won through indirect control of the center, challenging Tarrasch's dogmatic view that the center must be occupied by pawns. Nimzowitsch advocated controlling the center of the board with distant pieces rather than with pawns, thus inviting the opponent to occupy the center with pawns, which can then become targets of attack. However, this was only part of the hypermodern framework, which Nimzowitsch encapsulated in the seminal chess book My System, which greatly influenced many chess players. It introduced and formalized concepts of the pawn chain, overprotection, undermining, prophylaxis, restraint, rook on the seventh rank, knight outposts, the dynamics of the isolated queen's pawn, and other areas of chess.
Hypermodern openings include the Réti Opening, King's Indian Defence, Queen's Indian Defence, Nimzo-Indian Defence, Grünfeld Defence, Bogo-Indian Defence, Old Indian Defence, Catalan Opening, King's Indian Attack, Alekhine's Defence, Modern Defence, Pirc Defence, Larsen's opening, Sokolsky Opening, and to a lesser degree the English Opening. Openings such as 1.a3 do not constitute hypermodern openings since, although they delay the occupation of the centre with pawns, they also delay piece development.