You can do one of two things:
You can select the 'Move' tool in the toolbar (T) or press Shift+Space> G:
If you would like the gizmo to appear regardless of the tool you have selected, click the 'Viewport Gizmos' button in the 3D View header, enable gizmos for active object by enabling the 'Active Object' option and then enable the 'Move', 'Rotate' or '...
To fix the . shortcut, press N to bring a sidebar, go to View > View Lock and disable Lock to 3D Cursor
As for the rotating pivot point problem, you can change that at the middle top of the 3D Viewport.
This is probably due to viewport display settings.
Select the concerned object and in its properties panel,
go to 'object properties' tab
then 'viewport display' section
and uncheck 'wireframe' check box
There's a setting for that under Main Menu > Edit > Preferences > Navigation Tab > Orbit & Pan choose: Orbit Method: Trackball
Otherwise Blender will constrain you to turntable rotation, which does not allow full free rotation around all axes (it keeps the Z-axis upright while rotating).
Unfortunately, I don't believe Blender supports right-click panning due to the use of right-clicking for drop-down menus or selecting. However, you can change the default MMB action to pan, and Shift+MMB will become orbit.
You parented the rig to the body.
But you should be parenting the body to the rig, so you select the body then hold SHIFT and then select the rig (in object mode) then press CTRL+P then choose with automatic weights. After that try moving the bones in pose mode.
Don't forget to let me know if that works or not.
You might have to remove the first parent to ...
As far as the hiding of the strokes goes, I have found a solution:
For whatever reason, the wireframe view was selected.
This problem was solved by selecting any other view in the top right corner (e.g. Solid view).