The MVP is determined by who gets the most kills. The affection point gained from a heroine being the MVP only applies if she's been racking up kills while in Nozomu's party. If a heroine becomes an MVP while an All Rounder, or in a different party, the affection point isn't added.
The sand clock is available in Katima and Satsuki's Artifact creation list. 時の砂, I think that's the one, can't remember the exact kanji so I'm going with what I remember.
My advice is to try your best to grab SS rankings in every mission, and unlock Nozomu's Aura Shield 2 ASAP. It'll save you a lot of frustration in Chapters 3 and 4.
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