Q: How can I get airdrop on an iPad 3

You can't. The iPad 3 does not support AirDrop due to hardware limitations.

As explained in the link you came from:

• iPad (4th generation) or later

Share content with AirDrop from your iPhone, iPad, or iPod touch - Apple Support

What you need

To share content with AirDrop, both people need one of these devices using iOS 7 or later, or a Mac with OS X Yosemite or later:

• iPhone 5 or later
• iPad Pro
• iPad (4th generation) or later
• iPad mini or later
• iPod touch (5th generation) or later

alternative to airdrop.

I use

"Dukto is a simple application that allows you to share files between devices connected to the same (wireless) LAN network."

http://www.tidal.it/?page_id=309&lang=en

http://www.msec.it/blog/?page_id=11

also lots of similar apps. example.

"Transfer files the easy way, just drag & drop the file and we will handle the rest. Like Apple AirDrop, but works and on all major platforms and computers that don't support AirDrop. Apps are available for iOS, OS X, Windows, and Android."

https://itunes.apple.com/us/app/instashare-air-drop-transfer/id576220851?mt=8

No. AirDrop has nothing to do with your Apple Tv at all, and RCcharles options will not connect your iPad to an Apple Tv.

I believe what you are looking for is AirPlay.

Your 3rd Generation iPad is perfectly capable of handling both AirPlay and AirPlay mirroring if you want to see what is on your iPad's screen on your TV via your Apple Tv.

Use AirPlay to wirelessly stream content from your iPhone, iPad, or iPod touch - Apple Support