I think you can delete these keys:
KEY `data_start` (`data_start`) -- redundant served by KEY `lista_przeloty` (`data_start`,`catalog`,`lotnisko_wylotu`,`kod_obiektu`)
KEY `catalog` (`catalog`) -- redundant served by KEY `shortIdx` (`catalog`,`kod_obiektu`)
KEY `kod_regionu` (`kod_regionu`) -- redundant served by KEY `catalogRegionIdx` (`kod_regionu`,`catalog`)
KEY `kod_panstwa_ISO` (`kod_panstwa_ISO`) -- redundant served by KEY `dlaPeriodow` (`kod_panstwa_ISO`,`catalog`,`kod_obiektu`) and KEY `lista_obiektow` (`kod_panstwa_ISO`,`data_start`,`catalog`,`kod_obiektu`)
KEY `period` (`period`) -- redundant served by KEY `dlaPeriodow2` (`period`,`catalog`,`kod_obiektu`)
KEY `catalogRegionIdx` (`kod_regionu`,`catalog`) -- redundant served by KEY `lista_obiektow2` (`kod_regionu`,`catalog`,`kod_obiektu`)
KEY `dataCatalogIdx` (`data_start`,`catalog`) -- redundant served by KEY `lista_przeloty` (`data_start`,`catalog`,`lotnisko_wylotu`,`kod_obiektu`)
This won't help you with the select, but will help overall since you are just cluttering up your design with redundant index data.
Once I see the create on the other table we can go from there.
Shawn