what should be odom broadcast frequency for slam?
My odom is being broadcasted at a rate of 10 Hz currently? Is it good enough to run a turtlebot-like robot autonomously?
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Depends on your application and how fast everything is running. I typically recommend as a blanket 100hz, but really you're limited by the "fastest" thing happening. If there's something trying to get the pose of your robot at >10hz, you're going to get stale or interpolated information.
100hz for a typical ground robot running the typical ros navigation-like things is usually fine. That may be going overboard depending on your application. 30hz is a good hobby-number if your encoders have enough ticks to make that meaningful.