22/7, Paris 9:06 - Mainz 13:18 (change at Mannheim Hbf ):
Paris - Mannheim: reservation mandatory. Can be done online via Eurail.
Mannheim - Mainz: reservation optional. I wouldn't bother.
23/7, Mainz Hbf 0:41 - Kraków Główny 17:07 (change at Wien Hbf and Břeclav):
Mainz Hbf - Wien Hbf: reservation mandatory, best done via ÖBB using these steps.
Wien - Břeclav: reservation optional. There are a few trains to choose from to catch the 12:10 from Břeclav.
Břeclav 12:10 - Kraków Główny: reservation mandatory. Can be done via Czech railways. Price is 75 CZK (~3.07€). You have to add the discount card Eurail Global Pass. In the results, you'll see a link "I want a reservation only”. Click on it, wait for the price to appear and then confirm.
27/7: Kraków Główny 10:01 - Warszawa Lotnisko Chopina: I see you used the rail planner app to get this timetable. Unfortunately, the timetable in the app is outdated because it doesn't get enough updates. Better is to plan with local planners (such as this one for Poland) or the German railways planner for international journeys. In addition, the Polish planner warns that there's a timetable change on 12 June and there will be changes, so it's better to check again by the beginning of June. Domestic tickets can usually only booked a month in advance, so there's no rush to get a reservation.
Eurail is not valid on the suburban trains in Warsaw, i.e. the one you would be using between Warszawa Zachodnia and Warszawa Lotnisko Chopina.