You would definitely be better off investing in the home-country mutual funds than doing cross-border investment.
If you're investing through a broker in your home country - I expect that broker would tell you what paperwork is needed.
If you're investing through an American broker, you'll have to file a form W8-BEN with the broker, and claim whatever treaty benefits you may be eligible to (talk to a tax adviser in your home country who's familiar with the US taxation). Unless there are specific treaty provisions, you'll pay US taxes on dividends and will have to file a US tax return if the dividends amount to more than several hundreds dollars a year. In fact, you'll probably have to file a US tax return even for lower amounts, since by default the payer will withhold 30% of the dividends on behalf of your taxes - which is most likely much more than your actual tax on these dividends. You'll have to file a tax return in the US to claim the refund of the excess amounts withheld.
The treaties are between countries. Europe is not a country but a continent, neither North America nor the US have any treaty with Europe.
If you're a college student with minimal amounts to invest, I seriously doubt you would be unable to find a suitable local fund.