The exercises including pitch in EarMaster are training your relative pitch recognition skills. Perfect pitch is not included as standard training, but you can customize EarMaster to train it. Therefore, you can be sure that unless you set it up otherwise, EarMaster will train your relative pitch skills.
For your last question, the short answer is yes. Having good relative pitch skills will help you identify chord qualities (Maj, min, dim, 7, etc.) and the pitch relations between each chord, especially with the exercise on chord progressions.
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