Roku TV includes Roku support inside (device). Roku device/service itself does not support Chomecast, & last I checked does not mirroring of screen/display from computer/smartphone/tablet (another answerer said it does, perhaps they know better?). The TV may be able to support Chromecast or screen/display mirroring, if included or else by adding an external device (usually via HDMI). If you want screen mirroring ability at all (not only Chromecast), check the TV manual or manufacturer for options, to see if any means included (Chromecast, Miracast/MHL, even Wi-Fi provides wireless options). If not included, ability can likely be added via external device &/or software. Also same for device you are sending/transmitting/mirroring from; may be included options.
No
Yes, you can transmit from your cell unless off course if it's not supported
Roku is a streaming service provider provider similar to Chromecast/Amazon Firebox/etc. It hooks you up with various providers like Netflix, Hulu, etc. A Roku device is capable of receiving chromecast from a cell phone via screen mirroring, if you wanted, but unless you're mirrorng something thats not supported by Roku i dont see the point. I'd suggest googling roku supported services for more info.
Thanks! Your answer is awaiting moderation.