"My hands got tired because I carried a heavy bag."
True, it's more like "My hands got tired carrying a heavy bag." While the Japanese sentence is fine as is, the explicit 'because' in English trips you up. To have it to be more of a sequence of events with an implied 'because' in English, the translation would have to change too.
I disagree with this translation. The use of "because" wouldn't be needed unless it's describing a direct causation between two events. Implications (as in the absence of because) would also imply that other causes could exist. Without から present, the sentence seems more like "my hands got tired after I carried a heavy bag." Notice how there's no indication of direct causation. This is what because is for.
I would say no. I think its wrong because you don't use past form here
sentence like 重いかばんを持つから手が疲れる would mean that hands will get tired because you will carry a heavy bag.
重いかばんを持ったから手が疲れました I translate as My hands got tired because I carried a heavy bag