1) If you link the new Roku to the same user account as the existing Roku, all channels installed under that account will be automatically installed on the new one. In some cases the user credentials will also be passed, but with others you'll need to log in again. If you remove a channel from one device, it will be removed from the other as well. They are linked that way. You can arrange the tiles differently on the two devices, but they will always have the same channels installed.
2) If the older device is connected to a Roku TV, you can simply select the HDMI input you connected the older Roku to and watch that Roku. Remember the two remotes won't control both devices. The TV remote will still only control the TV and the player remote will only control the player. If the player remote has volume buttons, it should be able to control the TV volume through CEC. If you are referring to a really old TV that has a Roku Stick built into them (it still operates like a Roku TV, but has separate inputs), you should still be able to use the Roku player the same as mentioned above.
Depending on the Roku TV you are referencing, and how old the original Roku player is, you might not see much of a performance improvement with the Roku player. But if the TV is one of the older ones with the Roku Stick built into it, you absolutely would see an improvement, as those older Sticks are no longer supported by Roku and many channel developers are removing support for them as well.
Roku Community Streaming Expert
Help others find this answer and click "Accept as Solution." If you appreciate my answer, maybe give me a Kudo.