They are complementary rather than comparable. Abhijit is a time-based window (midday Muhurta from roughly 11:48 AM to 12:36 PM) that occurs daily. Dwipushkar arises from a rare three-fold astronomical alignment. Experienced practitioners often seek both simultaneously - an Abhijit window within a Dwipushkar day - for the most auspicious combination.

Classical texts are divided on this. The general guidance is that Dwipushkar's power is great enough to significantly mitigate - though not completely cancel - Rahu Kaal's unfavourable influence. When possible, plan important actions outside Rahu Kaal even on Dwipushkar days.

The Pushkar tithis for Dwipushkar are the 2nd, 7th, and 12th lunar days - in both Shukla and Krishna Paksha (tithi numbers 2, 7, 12, 17, 22, 27). Amavasya is the 30th tithi. Since Amavasya is not among the Pushkar tithis, Dwipushkar cannot coincide with Amavasya.

Pitru Tarpanam is traditionally performed on Amavasya, which cannot coincide with Dwipushkar (different tithis). However, on Krishna Paksha Saptami or Dwadashi Dwipushkar days, performing ancestral rites is considered especially meritorious by some traditions, as the Pushkar quality enhances all sacred acts.

Tripushkar Yoga requires the simultaneous alignment of all three Pushkar elements - Pushkar Vara (Sun/Tue/Sat), Pushkar Tithi (2nd/7th/12th), and Pushkar Nakshatra - but with the additional condition that the weekday's lord's nakshatra is also involved, creating a triple resonance. Dwipushkar meets two of the three primary conditions; Tripushkar represents the complete, triply-validated alignment. Both are rare; Tripushkar is rarer still.

Yes - Tuesday and Saturday are among the three Pushkar Varas. This is worth emphasising because Sarvarthasiddhi Yoga has restrictions on Tuesday (vehicle purchase) and Saturday (iron/oil). Dwipushkar has no such restrictions; its energy transcends the weekday-specific limitations of the other yogas.