do I need to line the bottom of my raised veg plot

dont line the bottom with anything , fork the ground and turn it over then put the raised bed on top , root crops send out a tap root that will not like hitting a membrane at the bottom of its world.

What is your raised bed sitting on? If it's on soil, I'd say no, if it's on tarmac/concrete I'd say yes, it will help retain moisture and reduce the need for watering too much.

depends on how deep this raised bed is.
if it's 18" deep then you could put down a layer of weed control matting , which would allow for drainage . but stop any weeds / roots from coming up into the bed.

Hi , we did not put anything at the bottom of our raised beds, and everything doing fine
good luck