During showdown Chakram Dancer is played from hand at reaction speed, opponent uses Star Cross. Does the effect of Chakram Dancer still on the chain and give +1 to defenders even if she's sent back to hand?

No — the Shield is not granted. Chakram Dancer's trigger is still on the chain and does resolve (it's an independent object), but it says "give your other units here [Shield]," and "here" refers to Chakram Dancer's location. Since Star-Crossed resolves first and returns her to hand (a non-board zone), "here" returns null at resolution and the instruction is ignored (Rule 359.3.f.2, FAQ #3430).

This is the same principle as the Yasuo ruling: a "here"-dependent play trigger mistargets when its source leaves the battlefield. Contrast with effects that don't reference the source's location (e.g., "enemy units get −3 Might") — those would still fully resolve.