Not really. as the schemes of the prideful and long-lived (oe unliving in this case) usually look long into the future as opposed to the short-term. This mirror seems to focus on a short-term, immediate future. It'd would be of minor use to Remilia at best. Learning how to divine the long-term, however would give her ample time to manipulate fate without using her power. That said - would she care to?
I'm really confused. The cause of Marisa's death was Alice's cold because she wouldn't leave Alice behind when Gensokyo was destroyed, but they stopped Gensokyo from being destroyed, so how did Marisa die? And if Gensokyo's destruction killed Marisa who stayed behind due to Alice's cold, where are they holding a funeral? Gensokyo was destroyed.
Well, the panel did say "the original fate", which implies it was the fate before they prevented Gensokyo's destruction. It also implies Marisa and Alice would have spent time together regardless of the fate of the land, thus leading her to catching the deadly cold.