Well you are right, good results in the last 5 matches will be a consideration I'm sure Ten Hag will be given the opportunity until the middle of the season this means he still has time to prove his ability as a coach, I heard from several media that Manchester United will make changes to the management, Sir Jim Ratcliffe as a new investor wants to fix internal problems and transfers lately and this is a good step to bring Manchester United back to competition. As you said lately Manchester United often bring players who are not as expected and this is the main focus for Sir Jim Ratcliffe.
Regarding the Champions League, actually Manchester United still have a chance to qualify as long as they can win in the last 2 matches one of them has to beat Bayern Munich in the last match but before that Manchester United also had to go through matches in the Premier League against Newcastle and Chelsea, obviously this is a challenge when they need to win every match.
Yes, at least that can be a consideration, I think Ten Hag's management is good, but maybe Ten Hag recruited the wrong players, causing Manchester United's condition to become unstable like this.
it turns out that there are still many who believe in this coach and believe that Ten Hag will slowly start to improve it, Manchester United just need to be a little patient to be able to achieve optimal results, Manchester United must learn from last season where they experienced a decline and they recruited Ten Hag to become coach and immediately improved this team and in the end Ten Hag was able to improve Manchester United's performance slowly and I am sure that this season Ten Hag will also prove that he is capable. Ten Hag is a coach who is fearless.
Talking about the Champions League, Manchester United still has a chance, but it's only a small possibility because Manchester will face 2 big clubs who previously beat them, but if Manchester United can avenge their defeat, Manchester United will be able to qualify for the round of 16, but in my opinion, Manchester United has a chance are only in 3rd place and play in the European league (if they can).