No, tänka means to think as in using the brain, or to state intention. We use tro for thinking in the sense of believing.
It's like this:
- tro = infinitive
- tror = present
- trodde = simple past
But the song you mention contains the line Ur vad jag trott, where trott is the supine form.
It makes sense, it just doesn't translate this sentence. 'I thought that you went home' would be Jag trodde att du gick hem.
So would gick be the only word to use in that sentence or is there another word that means went as well
Either gick or åkte, gick if you more or less went on foot, åkte if you travelled using some vehicle. If you went home to another country it would be åkte hem for instance, gick would sound funny, but if you leave a party to go home, first on foot, then taking a bus for instance, you could use either. gick would be the preferred one, åkte would emphasize that you used some vehicle.
TTS "ja troddate vor hemma" do swedes say it like tts when they are talking fast?
Kind of, yes. Most languages blur words together, and Swedish is no exception. I'd use another approximation, though.