Baking – Can cake batter sit before using

To me, the definitive guide to all these gelling agents is "Texture", the free e-book at khymos.org (which I know about because of this site, by the way). It says that mango is an inhibitor to the working of gelatin, so gelatin won't help as much as you might hope. Having said that, some of the example recipes do use gelatin, so it might still help enough.

About guar gum, it says that acidity (low pH) is an inhibitor; are there any acids in your mango puree? It also says that guar gum leads to high viscosity when warm and low when colder, so cooling it down should definitely make things more solid. You could also try some of the other agents; maybe xanthan gum will help.

Don't most cake recipes require mixing dry ingredients first? Well, what's been done has been done.

The standard professional chef way of getting lumps out of anything is to pass it through a fine strainer. In your case a standard metal pasta strainer should work. Put the strainer over a bowl, pour the batter in and use the back of a large spoon or ladle to gentle press the batter through. The lumps of sugar will be left over and you can just crush them then.

Whipping the batter might work the gluten proteins in the flour which will make for a tough chewy texture. Some cakes actually take this into account and others it is bad, so be careful.