Translation:She usually wants to swim in the morning.
Ah, tack. Yes, with your help I found it. Here, please take a lingot. http://quizlet.com/71396393/duolingo-swedish-verbs-infinitive-1-lessons-1-4-flash-cards/
Yes, it's tricky. I also did Pimsleur's Basic Swedish course (ten lessons, audio-only). They have sentences such as "Jag skulle vilja ha något att äta" and similar ones, which they loosely translated as "I would like to have something to eat." So, between that and the Google translate, I had thought vilja was more to like than to want. Is skulle the conditional of something? I had no idea that's how it's spelled; again, I used Google translate to find out.
Exactly - att vila is "to rest", and att vilja is "to want".
The j in vilja is an heritage from Old Swedish vilia, which is cognate with many related words, some of which retained the glide sound (e.g. Old Saxon wilian) and some of which didn't (e.g. contemporary English "will").
'Vill' and 'vilja' are different forms of the same word, like the difference between 'want' and 'wants' in English, or 'åka' and 'åker' as another Swedish example.
Swedish grammar says that after the verb 'brukar' (meaning 'usually') you need an infinitive verb, in this case 'vilja'.
I think a native speaker would understand your meaning if you said "Hon brukar vill..." and they'd take the same meaning as with "vilja", it's just not the proper grammar.
No, you can't say 'Hon brukar att vilja...' I assume it would be understood, but it's not grammatical. It would be like saying "She usually to want to swim..." In general, the 'att' disappears in Swedish with verbs like this, e.g. "Jag måste försöka!" or "Han vill leka".
Duo's notes on modal verbs might be clearer: https://www.duolingo.com/skill/sv/Verbs%3A-Modal/tips-and-notes
And by the way, 'brukar' isn't actually an infinitive, it's the present tense of 'att bruka'. I don't think I've ever seen 'bruka' anywhere outside of a dictionary, but I'm hardly well-read in Swedish! Maybe one could say something like "Han kommer att bruka..." to mean something like "He's going to be in the habit of..." in the future.