Hi Venkatesan, sorry to hear about your troubles.
Please keep in mind that AirDrop is a technology by Apple that allows users to share and receive photos, documents, and more with other Apple devices that are nearby. Please keep in mind that Apple has your security in mind, and allowing any non-apple device to send files/information can be used maliciously. Here is more information on How to use AirDrop on your iPhone, iPad, or iPod touch - Apple Support.
For screen mirroring, I suggest you check out Apple AirPlay feature. AirPlay is a proprietary protocol stack/suite developed by Apple Inc. that allows wireless streaming between devices of audio, video, device screens, etc. There are many AirPlay compatible devices on the market that are not produced by apple. Please refer to this page for information on AirPlay system requirements - Apple Support
The list of TV's and streaming devices that are compatible with AirPlay is constantly expanding. However, as mentioned before, Apple has your security in mind, so they will only approve devices that will not put your information at risk.
I personally do not think Apple has a monopoly in the screen mirroring sector. There are many non apple devices that can receive AirPlay data. However, it is impossible for every device to be compatible with AirPlay. The same goes for devices running other operating systems, like Android. Not all screen mirroring options are compatible for Android devices.
