It will with in the sense that it will pull in stations over the air. It works great, I'm using it with my projector which has no tuner. This box has hdmi and yellow red white, and coax output. The picture is fantastic over hdmi. I can't speak for the other 2 methods, but according to the(limited) included instructions, it outputs over coax over either channel 3 or 4, with a selector switch.
I am not sure about what you want to do with it. If you think you can record two shows simultaneously, then no. I use this with my VCR and it will only record the channel the Homeworx is set to. Likewise if you were to connect this to your Tivo, you could only record the channel the Homeworx is set to at the time. This would be true for any digital converter. The only reason I would connect a digital converter to a TiVo would be that the tuner was broken. You could possible bypass the tuner by using the red,white, and yellow inputs on the back.
Yes, there is a remote control that comes with the unit. It works OK. Sometimes remote is not that responsive but that may be the unit itself and not the remote control. BTW: One cannot record live programs to USB with this unit. I bought another unit higher cost unit (Viewtv At-163 ATSC Digital TV Converter Box and Media Player w/ Recording PVR Function / HDMI Out / Coaxial Out / Composite Out / USB Input) that can record programs to USB.
Well, given that it's a digital box, all the channels are digital. Now, if you mean regular versu HD then yes, this box gets both the regular channels and their HD version as well. You will need a good antenna though. Mine plugs in to boost the signal. I use the box to watch local TV channels on my HD monitor and I'm very happy with it. Btw, summer seems to be better for reception than winter for some reason. Good luck!