Hi Genete, thanks for your input, it is really helpful.
I try my best to explain it clearly

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These buttons have to behave as simple as possible.
[Erase] button:Erase is erase all. It will remove all rendered frames if they existed, and the "preview window" will return to the beginning: nothing rendered, all the buttons will be reset to initial state except the "Loop" button, it is staying as it was.
So the answer of Quesiton2 is rendering and playing will stop. these two buttons([Play] & [Render]) will reset to initial state.
[Render] button:"Render Start" always starts rendering from scratch, and "Render Halt" will stop rendering completely, and we will have no a state called "pause" for Render.
So the answer of Question1: once the user pressed/toggled off [Render] again, the [Play] pops up and the animation preview will stop at the same time, the time slide indicator back to the frame filled in the "From" entry.
[Play] button:Once [Play] button is toggled on, the scene will be start playing, when it is toggled off from previous state, the preview will have a pause state, toggled on again, the playing will continue.
[Loop] button:Nothing special, It affects "playing" behaves, but never be affected by the Render, Erase, Play buttons.
All these buttons will never be affected by "zoom in/out" the previewing scene.
more questions1) To have a "pause" for rendering seems nice, but I am not sure if it will help artists.
2) How about to bring "Seek to Begin/End, next/prev rendered frame" on preview window? Do these functions help the "preview" job?
3) The time slider, what the length it should have?
3.a) the entire of scene (canvas time)
3.b) the specified in the preview window via "From" and "To" entries?
3.c) the rendered time length (rendered frames)?
3)