It is two things here that are relevant for Chelsea. They are quite bad in away games because the five games you pointed out of which three games were lost were all games away from home. You can't afford being that weak away from home if the goal is to become a Champions League team next season. As you said they got some luck as Manchester City and Newcastle have similar problems, but Chelsea is only winning 33% of their games away from home. That's why it is kind of surprising that they are still top four.
It's because many clubs in this race are very inconsistent in this season, from Chelsea, Manchester City, Newcastle United and some other clubs. It's like a race among many inconsistent clubs to find a most consistent club that will take a fourth position at the season ending.
Chelsea are actually in a good situation for taking a fourth position in Premier League but they have big challenge from Manchester City and Newcastle United. Newcastle United played one less match and they are able to take over the fourth position from Chelsea if they win that match. At the moment, Newcastle United is a biggest threat against Chelsea and by beating Liverpool to win EFL cup, Newcastle United sent a strong voice to Chelsea.
In the remaining games they have to play against Liverpool, Newcastle and Nottingham. The other games Chelsea is the favorite I think. But Manchester City is away that they now need a perfect sprint to reach their minimum goal.
Every match is important but two direct matches with Newcastle United and Nottingham Forest will be most important for Chelsea. They can finish in top four or beyond it, even beyond top six if they get bad results from these big matches.