* FalseYou cannot convert an arc to a line by hovering over the center grip of the arc segment. You need to convert the arc to a polyline first, then use the FLATTEN command, and answer YES to remove hidden lines. Then you can explode the polyline to get line segments.
https://forums.autodesk.com/t5/autocad-forum/autocad-is-it-possible-to-convert-an-arc-to-a-segemented-li
* Falseyou can edit the polyline width by hovering over certain grips if they are vertex grips or midpoint grips. However, if they are arc segment grips, you cannot edit the width by hovering over them1.
Therefore, the statement is false.
https://knowledge.autodesk.com/support/autocad/learn-explore/caas/CloudHelp/cloudhelp/2015/ENU/Auto
* Falseyou can add a new vertex by hovering over certain grips if they are edge grips or midpoint grips. However, if they are vertex grips or arc segment grips, you cannot add a new vertex by hovering over them2. Therefore, the statement is false.