Yep qc1 should be mate immediately
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#12 is pretty cool actually, but buggy at the same time. Here's two (!) alternate solutions:
1.Qh7! Bh2+ (any other move results in 2. Qxe4+ Kb8 3.Qb7#) 2. Kxh2 Kb8 3. Qb7#
1.Rh3 e3 2. Qxb8! Kxb8 3. Rh8#

#12 is pretty cool actually, but buggy at the same time. Here's two (!) alternate solutions:
1.Qh7! Bh2+ (any other move results in 2. Qxe4+ Kb8 3.Qb7#) 2. Kxh2 Kb8 3. Qb7#
1.Rh3 e3 2. Qxb8! Kxb8 3. Rh8#
I would not say it is a bug it is just an alternate solution. It is still mate in 3. Anyway this first alternate also good, мне нравится.
No after 1.Rh3 e3 2. Qxb8! Kxb8 3. Rh8# black can move to 3. .... Kc8.

Yes, if you played for white
Qc1?