Implementing the interface methods should go first and then the rest, it may be that when for example I implement an interface first to that works and add the rest, then if I implement it later more after the rest will give error ...?
The order of the methods has no impact at the functional level. Although to have the code ordered and understandable it is advisable to structure it as you comment.
If you refer to a class that implements one or more interfaces, yes. It is necessary, first of all, to implement all the methods that define the interfaces in the new class in order for the class to compile without errors. The spirit of a Java Interface is to ensure that every class that implements it will comply with the "contract" that this Interface has defined in advance. This "contract" is only a series of methods that must be implemented (although the body of the method is blank) in a mandatory manner. In terms of performance, the order does not affect in any way since even the IDE changes the order of the variables and methods to suit the user, it will simply be easier and more animated, in coding time, to work in a class without compilation errors.