If it were anyone else it would be hopeless, but this is Alice so there is a better than average chance.
She's got Sedna, who is pretty much equivalent to her, damaged right next to her; she can't just assume she can handle this as easily as usual.
Alice can't win with brute force. If she could then she and Sedna would've dealt with Mr. Church instead of attempting to flee in the night. However, she knows more about the past than Mr. Pate and he probably knows nothing of the Praeses so this gives her some advantages, but she'll have to out think him which may be possible since like most villains his arrogance can outweigh his intelligence.
As awful as Pate is...is he worse than the Praeses?
Quite simply - we have no idea yet!
Indeed. This may all be a trap to bring the last of the immortals to a space habitat where they can nullify their abilities and conquer Earth without any trouble. Mr. Church is unbeatable on the ground, but if he is plunged into zero gravity or propelled toward the moon, Mars, or even the sun then it doesn't matter how powerful he is. Alice assumed she was all that stood in the way, but I doubt Mr. Pate would like it if the Praeses invaded without him being a part of the new world order. If the Praeses knew all of the people that would potentially thwart their plans and could eliminate them in one fell swoop this would be the best way.
I'm starting to think this will end like Eanbrain Tain's ill-fated preemptive strike against the Founders.