This isnt an exact answer to this question, but from a quick glance it looks like all of your questions could be solved by adjusting styles.
In this particular case my best guess would be by the use of lv_obj_set_style_boder_width and choosing a value of 0,
I would suggets having a good look through the style documentation to see what the options are and then if you still have questions you can follow up.
I am primarily a micropython developer and so am not 100% sure that this is correct, but whatever you are using to develop code (VS code for me) should have some form of intelitext to give suggestions about what style options there are.
Again I know this is micropython but as an alternative you could have a look at the simulator (found here: LVGL/MicroPython Simulator) and type scr.set_style_ into the prompt followed by tab, it will show you suggestions.
You could also have a look at edgeline, the beta doesn’t have all the features and widgets but it does allow setting styles and things like the border width are included.
So I have looked into it a bit, and tabview is a compound widget so it looks like you may need to change the border width of the button matrix.
I am not sure of the correct code in C but I have put together something in the micropython simulator which may provide a clue (look at the last line):