What exactly happens during the crossover
Q1 In each pair, do chromosomes have to be of the same length?


Yes, approximatively.


  If yes, does it mean that this length is the same for all humans?


Yes, approximatively.


  Do chromosomes in different pairs have different lenghts?


Yes. E.g., in humans, chromosome 1 is 294 millions nucleotides long while the chromosome 22 is only 50 millions nucleotide long.


  Q2 In which exactly place do they get mixed? 


These crossover can appear pretty much anywhere. The probability of a crossover to happen at a given locus (locus=location on a chromosome) is not a constant throughout the chromosome though. In any case, the crossover always (almost always) happen at the same locus for each pair of the chromosome. In other words, if ~3 millions nucleotides goes from the paternally inherited to the maternally inherited chromosome, then ~3 millions nucleotides goes from the maternally inherited to the paternally inherited chromosome.