Identify boring status on running engine

Is there a way to notice/identify whether my engine piston is properly and slightly moving in parallel wall for engine which is already fixed and running.

The only correct way is to disassemble it and measure the components.

I don't understand your question? That it is running demonstrates it has at least the minimum clearance, an indication of bore wear can be done by monitoring blowby, a cylinder leakage test, a compression test, and/or borescope inspection.

If you want to know the exact figures, you'll need to strip it down as David said.

You aren't confused because a cold, or cooling down, engine has a large gap at the crown to the bore, are you? That's required because the aluminium (AKA aluminum) has a much greater expansion than the bore when at operating temperature, so a much greater initial clearance is required..