What is the effect of soaking minced beef in milk

It is quite common to make meat loaf with milk-soaked cubes of bread, but I've never heard of tenderising meat with it. Having said that, some kind of fat is common for marinades (yoghurt for example), so it might work. I'd try it with full cream milk, not half-and-half.

I think the reason for soaking liver in milk is to make the taste milder, as lamb, pork and cow liver can be quite strong tasting.

I believe milk helps to absorb strong flavor from meat. It may also impart a pleasant flavor of its own, but I have not been able to discern this. I have never heard that it can tenderize meat, and cannot think of an explanation that would support this.

I have used milk to soak organ meat before cooking (beef kidney).

Maybe the purpose of soaking the ham in a cup of milk for an hour is to flavor the milk, which is then used as an element of the sauce that's included in the recipe.

Soaking chicken livers in milk is for drawing out the bad smell.