I remember the game of Liverpool against Newcastle when they were playing away and they were even with 10 men yet they managed to equalize from 2-0 to 2-2 at that game where Newcastle was at top performance at that time.Based on this no matter that Liverpool is playing against Manchester City I would not write them off from a big,huge surprise if they are able to win at Etihad stadium,statistics are good to be shown but I don't think we should rely to much on them because the teams are not the same as they were years before.I think a draw would be the most likely result during this game.
Newcastle this season is not the best example, because their game is not as stable as it was before and perhaps you are confusing something, because in the match with Newcastle Van Dijk get red card, and Liverpool was able to win this match 1-2 despite the fact that they I had to play most of the match with ten men.
It will be difficult for Liverpool at the Etihad, perhaps more difficult than any other team, but they have a chance to take points from City. Liverpool is a team of mood, you need to watch how they start the match.
I agree with you that Newcastle United is not stable this season unlike the way they were last season, this is because they are playing in the Uefa Champions League, and they are not used to such a situation. I think if they don't qualify for the last 16 of the Uefa Champions League they will be consistent in winning matches in the Premier League.
Liverpool might be able to get a point from Manchester City at Etihad Stadium because Manchester City is not at their best form this season.