- Halwa: http://en.wikipedia.org/wiki/Gajar_ka_halwa
- Indian sweets: http://en.wikipedia.org/wiki/Barfi
- Custard: Formed from readymade custard powder.
,Milk Tea, and Cake, in which items can white sugar be replaced with Jaggery?
Of course you can use jaggery in all of these recipes or in any recipe in lieu of sugar, but like all substitutions, they may not be perfect or one to one. The outcome and flavor profile will be slightly different.
Consider what jaggery is made of (per the infamous wikipedia):
The parts that are not sucrose are the parts that are interesting. How will they affect your recipe? What adjustments should you make?
In regards to the specific foods you have mentioned:
Note that everything I have written is based on the science, and internet descriptions of local food items I am not familiar with. You should also consult local recipe books, and find variations which use jaggery--or the lack thereof. That should give you some idea what is common, and how recipes using jaggery vary from those that don't for the same item.
Jaggery gives more sweetness than the white sugar. Jaggery is used for making sweetened pongal. Even it can be added to coffee instead of white sugar to get taste.
The primary difference between white sugar and jaggery is that white sugar is refined and jaggery isn't and is in a more natural state. White sugar is simply crystalised sucrose whereas jaggery is unrefined whole cane sugar which includes the molasses component that refined sugar has lost.
It's this molasses component that gives jaggery its brownish colour which refined white sugar has had removed.
Molasses gives jaggery a more caramel flavour over refined white sugar and is probably a far better, purer product to use in place of refined white sugar in the examples you give. But do bear in mind the slight caramel flavour jaggery will impart due to the molasses component.