It usually is still a bit soft when you first take it out the oven, but it should be dry and starting to brown around the edges and top - this is baked a little darker than regular shortbread to make it crisper. So more go by the color/dryness to judge if it needs longer. It will firm up as it cools.

I'm so glad you enjoyed and it worked well! And yes I can see a little salt working (though not too much, of course).

When you add the icing, it will be fairly runny as the icing is warm and you are pouring it over a warm base. Though it should still have a bit of thickness (so not like water, more like a semi-thick sauce). But as long as you have everything in there and the right amounts, it should firm up fine as it cools. If your room temperature is a bit warm, you can chill it in the fridge to help it firm up more though this can soften the base so I wouldn't do unless needed.

So glad to hear everyone enjoyed! We are all big fans here, too.

Hope they all enjoy!