Is it permissible to designate one reading of the Quran for learning (Tajweed and Tafsir) and another as a regular recitation without learning?

Your method of learning Quranic exegesis (tafsir) and tajweed is correct and beneficial, and it is close to the method of the Salaf (early Muslims). You can solidify what you have studied and then move on to the next stage, or divide your time between reading tafsir, rulings (ahkam), and regular recitation. The Companions (Sahabah) would not move past ten verses until they had learned what practical applications were contained within them. Merely reciting the Quran is an act of worship and earns reward, even without understanding. However, tajweed of the Quran is obligatory for one who is able, and it is permissible to recite with a fast pace (hadr) while observing the rules of tajweed, in order to increase good deeds.