I'm not Japanese, but I know a few places where I've seen this word used which might help to define it better.
When I researched the word 「投入」, I found that there are usually two predominant meanings.
The first would be "to invest" as you had previously stated. From what I have seen, phrases that carry this meaning usually involve money, resources, effort, and energy. For example, 資金、資源、努力、エネルギー. The important thing to remember is that things that are used with 「投入」in this way can be deposited or stored.
The second meaning that I saw meant "to be thrown into". Situations where this meaning was used involved realeasing a product into the market, being thrown into orbit, and soldiers being put in another area/country. For example, 製品を投入、軌道に投入、軍隊を投入、政策を投入.
So to answer your question, 投入 probably doesn't need to be only limited to a thin paper, but probably can be applied to something that you store/deposit/place in a container/invest. For this there is 投入口 which is close to "slot".
As far as 「投入場」, I honestly am not sure. However, I would guess it means something like "an area where you throw things into".