"Martians called their planet Zho'da..." (p. 26).
Did they? We must take SM Stirling's word for it! I know Martians who call their planet Barsoom and others, speaking Solar, not Martian, who call it Malacandra. But there are many races of Martians... CS Lewis casually informs us that HG Wells' Martians are very different from the real Martians. Of course they are!
Zho'dans have several similarities to Barsoomians:
"...traveling silks and furs..." (p. 27);
an ancient civilization;
(A longer list than I realized when I started to write it.)
How would Terrestrials seem to Martians? We should be able to deduce this but, of course, we need an imaginative writer, in this case SM Stirling, to tell us:
"'...they ooze. They're positively slick with water and mucus most of the time. You can feel it on their breath.'" (p. 24)
Earth is wet, Mars is dry... We should have been able to deduce that for ourselves.
How many Martian races does Poul Anderson present?
The War Of Two Worlds
"Duel on Syrtis" and its sequel
The Technic History
Are Martians mentioned in the Psychotechnic History? (I cannot remember off hand.) (Later: They are. See here.)