"The man loves the woman."
Translation:Mannen älskar kvinnan.
Yes, that would be the correct way to say "I love Swedish". If you were to use "älskar" about a person ("Jag älskar Peter") it would imply romantic love, same as in English.
When speaking about a person there is also the word "kär", which implies infatuation. "Jag är kär i Peter" means "I am in love with Peter", for example.
The är (is/am/are) and i (in) are necessary when you're describing who you are kär with, as "jag kär Peter" would mean "I in love Peter".
I'm afraid this is all a bit messy and confusing, since both kär and älska have multiple uses and constructions which mean different things. Kär in the purest sense means "dear", and from that we construct the word kärlek which is the noun form of "love".
Here are some more examples.
Jag är kär i Peter - I am in love with Peter.
Jag älskar Peter - I love Peter.
Han är mig kär - He is dear to me.
Han är kär i mig - He is in love with me.
Han är min käresta - He his my beloved.
Det är sann kärlek - It is true love.
Vi älskar varandra - We love each other.
Vi älskar med varandra - We make love to each other.
As you can see it's something you'll probably just have to learn as you go, and at least in the case of the last two you probably don't want to confuse them in casual conversation. :)
It doesn't really fit into Duolingo's model. It would overly complicate lessons and I think the Swedish course does a fine job of exposing Swedish prosody with listening exercises for a beginner.
Here's a video for you if you're looking for yourself: https://www.youtube.com/watch?v=lXp7_Sjgm34