Several things can be used: Lecithin, Non-Diastatic Malt, Ascorbic Acid, and so on. You can find lists online, like here: http://www.breadmachinedigest.com/tips/dough-enhancers-and-how-to-use-them.php
where can I buy bread improver
Dough improver is actually called bread improver. it is used in bread making and can be bought in supermarkets. You add the bread improver into the dough and it will make a better loaf of bread.
Bread improver is made from certain chemicals and enzymes, but contains no animal matter. So yes, it is not only vegetarian, it can be considered vegan.
See the link.
Bread improver speeds up the time that the bread takes to rise and ready for the oven. It was introduced in the 1950's when mass bread baking facilities came about to take the time from about 12 hours down to 2 hours.
Bread improvers help produce gas and retain the gas inside the bread.
Purveyor called European imports
Generally no. They are, for the most part, enzymes, and they aren't "bad" for health.
If you use anything other than bread it is no longer "bread pudding".
Yes, you can use citric acid as a substitute for vitamin C (ascorbic acid) in bread making. Both serve as dough improvers, enhancing gluten development and improving the dough's strength and elasticity. However, citric acid has a more pronounced sour flavor, so you may need to adjust the recipe accordingly to avoid altering the taste of the bread.
You need to use eggs when you do any type of bread. You can make bread without eggs. :)
No. Bread improvers are normally composed from emulsifiers, enzymes and ascorbic acid. Cake improvers are totally different. There are cake gels, which mostly give the aeration of the cakes. There is also the PentaCake (see the link below), which is multi-functional and gives the entire solution for industrial cakes with shelf life of several months.