For your first question, the second choice of ""Its power was based on international trade" is correct. Most countries do not have the article "the" in front of it. (There are a few exceptions.) Thus it should be "present Sweden". For a discussion on this subject see: https://www.bbc.com/news/magazine-18233844 https://www.engvid.com/english-resource/the-with-country-names-lakes-rivers/

Between "on the international trade" and "on international trade", I would go for the latter. But if you think about the meaning, the power probably came from its high volume or efficient way or some other characteristic of the way they did the trading - i.e. it does not mean international trade in general. So I think "its international trades" is better for your example. For example, you can say: Its power came from its (high volume of / massive / ...) international trades. For the second question, I think "Present Sweden" sounds better than "The present Sweden", since we don't normally put the article in front of a country name (except for some special cases). "the" is not necessary because each country is always understood as the one and only one in the world. But you could say "The present Sweden" (or perhaps "The present day Sweden) too, if you want to highlight how it is different from the past, for example.