Is (pure raw cold-pressed) tung oil food-safe (for cooking utensils)?
Almost certainly yes. Just to mention, almost any oil of vegetable origin would be as well.
There's a small chance of individual sensitivity to the tung oil, as there is with so many things, but in general tung oil is not something that people react negatively to.
I want to try soaking wooden spoons and such (things which will come into prolonged contact with hot food) in tung oil.
If you are seeking to make the utensils waterproof I'm afraid you won't be happy with the results of your experiment, but I encourage you to try it anyway and see the results first hand.
No oil used in wood finishing actually provides a really good waterproof finish. Pre-polymerised tung oil may come the closest, but oil finishes of all types (using oil only, not a blended finish with resins in it) are inherently water-permeable.
Partly this is because oil doesn't penetrate that deeply into wood except into exposed end grain so there's actually very little of it left in/on the wood surface.
There is a method to greatly increase the oil uptake of wood in a reasonable timeframe, one used to produce oil-soaked wooden bearings — in short you deep fry the wood, displacing water in the wood's structure with oil. But this leaves the wood permanently oily which I don't think would be a desirable outcome here.
Is it a good idea to add a small amount of orange oil (food safety)?
I don't think there's any benefit to using that but this is something you'll have to make your own mind up about after reading up on it.
Note: there is a problem in that "orange oil" will often not be what you'd assume from the name. Obviously the expectation is that it's oil extracted from oranges but there are products with that on the label (ditto "lemon oil") which are not that at all, but instead a type of finish or wood treatment (or furniture polish!) with a citrus smell. Some of them would absolutely not be suitable for application to something intended for direct food contact.
No finish is necessary
Gotta add this FYI. Wooden utensils, just as with serving boards and most cutting boards, don't need to be finished in any way to work well in their intended roles.
A long while back it was the norm not to finish things like this and while it's still done today in some parts of the world in the West the idea has largely been forgotten about, or pushed aside in favour of one or another finish... but a great deal of this is about making things look better. While there's nothing wrong with that as a goal it tends to go hand in hand with an idea that the wood needs to be finished, but very often the treatment does nothing to improve the serviceability of a food-prep item and might even negatively affect one or more attributes.