can i use 2011 imac as a monitor for apple tv?

I think the Apple TV has a HDMI output port, which is not a compatible input source on the iMac. But you already have the option to WiFi stream many sources of movies and TV stations through a web browser, even Netflix, just like the Apple TV does. Even though you don't have a remote, you can use a BT keyboard and trackpad on a small lapdesk to control your iMac from the couch.

And you have one the last models of iMac that has a built-in DVD drive, so you can basically use the iMac itself as a WiFi streaming and DVD player TV combo anytime you want. Note, that the resolution of standard DVDs are limited to SDTV, 480, but the iMac tries to upscale it. You will get a better quality picture if you stream HD videos. But on the 27" screen, even SD still looks pretty decent.

I suggest some higher quality desktop external speakers (headphone jack or USB or BT) with a subwoofer at least to improve on the sound of the built-in speakers of the iMac.

At one time you could get a TV tuner for the Mac, where you can plug in an antenna and receive Over-The-Air HDTV signals from local TV stations and use your iMac as a TV and a DVR. The Mac compatible versions of those are a little hard to find now. The Elgato eyeTV were some examples, but I think they got bought out by some other company, I don't know who makes Mac compatible USB TV tuners these days. Some more info here, I am not familiar with any of these products myself, just some ideas to consider:

https://machow2.com/best-tv-tuner-for-mac/

No, iMacs are not televisions, they are computers.