I think the absence of Harry Kane wouldn't really affect their performance in Bundesliga, I believe they can still able to win against Dortmund. As long as Muller and Musiala are playing, they don't have to worry against mediocre teams.
But when it comes to Arsenal in Champions League, I'm not convinced Bayern Munich will win. It's The Gunners games because the match will held in Emirates Stadium.
Since joining Bayern Munich this season Kane has become a very important player for Bayern Munich, after Lewandowski's departure to Barcelona a few seasons ago, Bayern Munich did not find the ideal replacement before Kane came, and I think this Kane managed to meet the expectations munchen as striker.
Losing Kane is certainly a big loss for Munich, especially now that they are starting to enter a tight and crucial match schedule, including in the Champions League.
Facing Dortmund is of course a difficult game for Munich, but I also think without Harry Kane Munich is still superior to Dortmund for now, yes indeed we admit both matches will be difficult for Munich including later against Arsenal, but don't you currently also munchen have some substitutes who might be able to replace Kane up front against Arsenal in the Champions League, Although Kane has been a very important player in Munich, I don't think Munich is a team that relies on individuals to win all these years, besides what you said before is of course true because after all, apart from playing Dortmund, Muller may still be disastrous for Arsenal in the Champions League.