How to distribute fillings evenly in flan/pudding mix

That is simply caramelized sugar that coats the dish before the custard is poured in for baking. As the flan is chilled, the moisture from the custard liquefies the caramelized sugar and results in the sauce.

If you're wanting to make it for other desserts and aren't making flan, then simply caramelize sugar and then add water to it. Be careful as the steam can easily burn you if you're standing over it. The sugar will seize up and then as it continues to cook the crytallized caramelized sugar will liquefy. You will then have caramelized sugar syrup.

Part of the problem could be the refreezing of the ice cream. You know when you take out ice cream, eat at it for 5 or 10 minutes and then put it back in the freezer...and then the next time you take it out, some of the ice cream is a little icy and bit grainy?

I'm not sure you can solve this if you use the same recipe. Instead, I would recommend using the highest fat chocolate milk you can find instead of using melted chocolate ice cream.

I really doubt the pudding didn't get dissolved completely. If that really was the case, you could heat the mixture before you put it in the pie crust.