it looks like it’s actually a Chinese elm rather than Zelkova (a common mislabelling tactic apparently) and whilst Chinese elm are commonly sold as indoor bonsai, they’re really not. It needs to be outside. Put it in a shady location and only water when it needs it - it won’t be using much water at the minute- but never let it dry out completely (use a chopstick to probe how wet the soil beneath the surface is).
My guess is it’s likely to be an issue of the roots staying too wet, what does the soil look like? A potting/muddy type soil?
Don’t repot it yet - doing so will further weaken a seriously weakened tree, but be mindful that it will likely need doing next spring. Get rid of that rock if you can without it pulling up the roots.