This is confusing for me at least... When you say you are writing with a pen, you don't use the proposition с (я пишк ручкой). If you use the prep с, i was told it would mean that the pen is next to you also writing as if it would be someone hanging out with you. So, in this this example, why not just saying Дима ест рис молоком ( without the proposition с). Do you get my point? Ot there's a rule that i missing may be....
с usually means that something is accompanied by something else. If папа с дочкой go somewhere it means they are both going there. If you eat рис с молоком it means you eat them both (and this is how we usually name such combinations of foods).
On the other hand, if you eat рис молоком it means you are eating rice by means of using milk as a tool.