Can I say,

(A) He has sandwiches for lunch.
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If I say,

(a) He eats a piece / loaf of sandwiches.
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A sandwich is two pieces of bread with a filling between them.

He could eat a piece of a sandwich.

He would probably be ill if he ate a loaf of sandwiches - a loaf is the term of a large baked piece of dough, from which pieces are cut for use.
If by 'piece of sandwich' you mean a whole sandwich, no. It is a count noun. He can eat a sandwich, some sandwiches, three sandwiches, whatever. It is not like cake, where you get pieces or portions. Each section is considered a whole sandwich. Take one big sandwich, cut it in half, and what you now have is two sandwiches.

If by 'piece of sandwich' you mean only a part of a whole sandwich, as Feebs suggested, yes.
If I say,

(A) He eats sandwiches with some milk as breakfast.
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Yes, that is correct.

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Can I say?
<already answered>
Can I say,

(a) He likes to eat sandwiches and milk every afternoon.
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