Ack, my villagers have run out of food completly!
I've got the lift installed, I've got one seed down but it's still growing. I'm about 45000 tech points off getting rid of the sharks, I have no children left, my Chief has made food for today and my honey/tree is bare!
I've paused the game for now, and will leave it until tomorrow/I get a reply (!)/I figure out what to do, in the mean time, will the trees and honey grow whilst it's paused? Or should I just wait 24 hours and get my chief to make more food - Then wait another day or two?

No food will replenish while the game is paused, nor will trees grow. The chief can make more magic food, but it won't be enough each day to support your tribe. If you have the lift repaired, why don't you use it to get another tree growing?

I will do, but I can't really wait around for the tree to grow, unless I wait for the Chief to magic up some more food to tide them over whilst it grows?
How long can a tribe survive without food for?

It depends upon game speed and how hardy your villagers are (some are stronger than others). The best thing to do is to monitor their health bars and pause it before anybody gets critically low. Then have your chief make magic food as necessary to sustain them (in that case, keep it on slow speed anytime there is actually any food available).