I used to have tiled floors at the old place ..the whole downstairs was tiled ( lounge, study, living room , kitchen, laundry) terracotta ones..not cold at all contrary to what people think .. the kids loved riding their trikes around the house as it was massive open living space 36 squares in all. we had a wool rug where the living area was so kids can lounge around.. I find tiles are easier to maintain than floor boards.A quick vacuum and mop is all it needed and it hid the dirt well..whereas floor boards collects dust and hair etc.. Timber floorboards are nice to look at..the floating /laminate looks cheap and nasty I'd rather tiles instead.

Depends on the installer and what bamboo they're using.

I have a hallway with tiles and wanted to know if I can lay cork flooring over the top of the tiles

I’d go with timber or cork. Cork is great in a kitchen. Easy on your feet and joints and things are much less likely to break if you drop them. Especially as you age, tiles cause fatigue if you are standing in the kitchen for too long. Cork is now available in lots of different colours and styles including charcoals and greys that might compliment your slate. It’s not all 80s orange. Of course timber can look great too. Just make sure it’s ok for kitchen use.