Urea does react with nitric acid. It is used to destroy nitric acid in aqua regia before gold is dropped. Other things are also used but urea is quite common in industrial settings because it is inexpensive.
Kind of. Depends on how you describe "reaction".
If you take urea and plain nitric acid, mix them together in solution and wait, you will obtain urea nitrate. This is ordinary salt. Urea is basic, nitric acid is acidic, thus you will create salt of the aforementioned two. Similarly as you mixed nitric acid and ammonia. Or nitric and sodium hydroxide.
This, in chemical terms does nothing interesting in terms of nitric removal from solution. It just transform free nitric to nitrate.
In AR solutions however, nitric acid is decomposed by reaction with hydrochloric acid to chlorine and nitrosyl chloride. And only these two can actually react in some redox reactions with urea to chlorinate it, nitrosate it, eventualy diazotize the urea nitrogen and be extruded as elemental nitrogen (this is that familiar fizzing).
This sequence of reactions is very complex, leading to very strange intermediates and products, such as formamide, chloramines/nitrogen chlorides (nasty stuff), carbon dioxide, in some scenarios even carbon monoxide...
And all in all, this just do not prevent active oxidizer - chlorine - to re-dissolve gold in most scenarios. As urea does not reduce gold from solution, this "theatre" of often questionable and non-plesant reactions do not stop active species of AR from re-dissolving gold. It just supress it.
Most of the times, diluting of the solution can actually prevent significant re-dissolution of gold, if paired with urea. But I do not like the wannabe chemistry (without replicable reliability) to be performed on larger scale.
Of course you will obtain gold powder in the end. But remember, analytical significance of stannous Au detection in heavy metal chloride solutions has quite some limitations. And fact that you cannot see stannous "positive" does not necessarily mean you have all of your gold dropped.
BTW, I opened links you posted, but this is just a general promo and product sortiment of the company (what I seen, maybe it is there somewhere). Does it somewhere say something about the process ? Or do you have this information from some insider ? I doubt that such company will publically disclose it´s secretive setup and procedures. Urea can be used as additive in some electroplating baths, so maybe that´s it.