Staircase: I wud advise u can lay laminate flooring where u dun need hacking & hassle free if u r concerning de beauty of ur interior designing.

Remarks: mat doesn't look nice while non-slip tape will not last long for human traffic.

meanwhile fluorescent change 2 down-light without plaster ceiling is impossible.down-light is designated 2 have plaster ceiling & comes with few diff sizes..4",6" & etc.