It may be bad style for written texts, but the subtitles represent the spoken word and if you have 5-6 English subs starting with “I have” “I did” it’s way better to start the second sentence with “And” or “But” “Therefore” and other conjunctions, in order to provide a variety which prevents the subtitles to become boring. If someone would start so many sentences of a conversation with “I” others could easily mistake him/her for selfish and egocentric. 
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So true! I can now even use words which in the past would be dismissed by my teachers, cause it was “spoken language”. I can translate the word “nothing” with “niks” instead of “niets”, cause it’s something you commonly hear people say, but on a written translation test I would have lost points for it.
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indeed they do. I don’t have an issue with it in the context of what we’re talking about but starting a sentence with conjunctions such as ‘and’ isn’t something we would typically do in great British English, even in spoken form, although that said, it’s not considered to be as much of a linguistic transgression as starting a sentence with conjunctions in written form. Your English teacher would probably cringe instead of giving you a thick ear.
I just realised in my post above I didn’t actually state written form. My apologies.
I’ll edit it in a second
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I duck and run fast! 
I am such a disobedient student… I was often sent to the principle’s office. 
Then again, Most Americans don’t start their sentences with ‘And’. Just a subset speak that way. It’s also disappearing as younger generations get further away from their ancestral languages.
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