He isn't saying that a woman would not have started the war. So either he claims any woman leader would be so incompetent that Russia would lose the war, or so competent that she would win the war faster (which would according to him be a good thing).
I'm sorry, but that's not true. He uses the antisemetic term you said, but Marx also uses the phrase "Der jüdische N----- Lassalle." He used the English n-word in his letter. Check it out (best German version I could find):
https://www.iisg.nl/collections/herzenstichting/marx.pdf
I remember Marx also used the word in another letter to Engels about the American civil war, saying something like "one n----- regiment could muster up morale among northern soldiers." I can try to find that one too if you want.
Marx knew what to say publicly and privately. He knew not to use racist terms in his public writings since he didn't want to muster racist organization. He publicly kept his disagreements with Lassalle purely on theory and practice.
Ah, I had never read that letter before, thanks! Until this point I had only seen the Itzig passage quoted in this context, so I thought ppl were mistranslating.