A CruisRon and Karuna that for some reason did not have fighter cover (didn't really understand the start of the mission) whilst the Carthage was protected by fixed beam cannons and AWACS.
Wait, since when did they not have fighter cover. It's not because it's all gone when you arrive that they were never there ?

Serkr team was on standby to engage the Toutatis, deploying them against the artillery would have forced the UEF to withdraw.
1) The Narayana had their drives ready. Serkr wouldn't have had time to kill them.
2) Deploying Serkr against the artillery would probably have left another critical target wide open for the Toutatis to attack. Subspace chess, remember ? Re-read the briefing of this mission. Steele wants to avoid escalation before he is ready for the big battle. Especially if escalation doesn't happen on his terms.
3) They are deployed against the big T if you've ****ed up because for Steele, such an opportunity to destroy the big T is more important than keeping the strategical momentum. Steele can definitely afford loosing a couple days prepping Serkr again if the big T is out of the equation.
4) A Solaris down would be much more a major blow to the UEF morale (and leadership, if Calders goes down with the ship) than two more artillery frigates, of which the UEF has already lost many since the beginning of the war. The Vikrant and Toreador simply don't hold a comparable strategical value than the big T.
Serkr have sprint drives - they could get out before Calder could do much damage
Yes, and Steele would have lost momentum again, for no gain.
The fact that she was left in command is explained as: hers were the only forces on station and Steele didn't want to slow his build up by deploying more assets. Fair enough but that would not stand up in a military tribunal. Lawyers would pick holes in the decision to place her forces in harms way and ultimately the blame for the loss of the Carthage would go back to Steele.
You underestimate Steele's charisma and influence. Remember we're talking about one of the most powerful man in the GTVA, someone that could dictate terms to Tocqueville. The GTVA is more concerned about winning Sol than holding a trial against him, especially when he's the only man that can give them Sol fast enough. Whatever arguable strategical decisions he may take, they can overlook them, as long as the situation in Sol is finally resolved. And he'd get a few medals afterward, too.