Room lights flickering when I connect my desktop computer when running on Inverter
Your desktop computer's PSU draws electricity in a more complicated way than something like a light or fan does. Nothing's really working incorrectly... it's just that the inverter and the power supply weren't built for each other. The power supply is sucking power when the inverter doesn't expect it, causing a dip in the voltage; then the inverter up-regulates the voltage to compensate, only now the PSU isn't drawing any power and the voltage goes too high.

Replacing the PSU with one that does "power factor correction" may fix things. (Be careful - manufacturers of cheap PSUs will flat-out lie about whether a PSU does power factor correction, as they lie about other specs. Buy a trusted brand.) Alternatively you can use a voltage regulator, such as this ugly little box, to isolate the weirdnesses of the PSU and the inverter from each other. A good voltage regulator like that one will instantly solve a wide range of power issues. (I swear by the APC Line-R, but other people prefer the Tripp-Lite brand.)