As the title says: If I have more than one light in my scene
the first light is fine,
the second is barely visible,
and any after that basically don’t project any light.
And the light that my player is ‘holding’ doesn’t have a pool of light at all but still shows light on walls and pillars.
Here is a screen shot which should be colour the same way as the text above.
It’s your pixel light settings. Rendering lights per-pixel takes a fair bit of processing power, so Unity is trying to optimize it by mostly only rendering the brightest one.
You can fix it by allowing more pixel lights: Edit → Project Settings → Quality, set Pixel Light Count to at least 4. It’ll be on two at the moment which is why you’re not seeing the third light at all.
Alternatively you can fix it by just telling Unity that rendering those lights properly is important. Select all the spotlights and set their Render Mode property to Important.
If some of your spotlights don’t ever move, consider baking them into lightmaps: Unity - Manual: Lightmapping: Getting started
You might be able to get away with only having one dynamic pixel light anyway - the one on the player.
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I don’t know about iPad specifically, but generally you’ll want to bake (lightmap) as much of your lighting/shadows as possible, as obviously have fairly low poly counts.