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I'd say they mean pretty much the same. "была растрогана" seems a little bit stronger than "была тронута"and "растрогалась" seems to be the strongest (probably because it's active) and I woudn't use...

Я была растрогана is quite common, I woudn't use "я растрогалась" here.
"на (свою) родину" or
"к себе на родину"
another version is: Моя новая мечта - вернуться на родину
Another version is "Ты...