Manchester United will definitely going to be having a long ride in the coming weeks regarding their fixtures, lol. They will face an inform Nottingham Forest and after face one of their fierce rivals Manchester City although City is currently dip in form, maybe they might breath a little.
How many points do you expects from the Red Devils in the remaining games? Can they be able to move forward from the 13th position? Let's see how competitive they can be this season. Manchester United upcoming fixtures becomes tougher because the oppositions coming their path are not average but consider to be competitive. Manchester United will face Nottingham Forest, Manchester City then Marseille Lyonnais in the Europa League. You see there's more complicated scenarios for the manager, Ruben Amorim.
I think nobody can really tell how many points Manchester United will be able to take in their remaining matches in the Premier League, but if there is a positive change in Manchester United's pattern of play and they win more of their remaining matches in the Premier League, they will surely finish in the top 10 in the Premier League table. Nottingham Forest is more consistent than Manchester City in the Premier League, so I see Nottingham Forest as the only tough challenge for Manchester United in their next two matches in the league, but with the late improvements that Manchester United has shown, there's a chance for them to get a positive result against Nottingham Forest if they maintain the same performance they've shown against Arsenal, Real Sociedad, and Leicester City.
You are right in your analysis Manchester United has improved their style of play viewing from their past mentioned game if they continue winning game they will surely finish top 10 in the table but i doubt if they can be able to get a draw in the hands of Nottingham Forest because this team is currently performing unbelievable in the English premier league, they have really surprised people this season in the English premier league no one will be believe they will be among the top 3 teams in the premier league table but for Manchester United winning Manchester City is possible because Manchester City this season is not even consistent in their games it will be tough though because Manchester United too is not consistent but they has more better opportunity to win Manchester City.