Does this sentence make sense?
我一連犯了好幾個事情
Yes, but the grammar is odd.
Not really. 事情 aren’t really something you would 犯. Grammar is fine, but usage is off. You could say: 我一連犯了好幾個錯誤.
I don’t know, 事情 has a negative connotation at times. Not to say it’s standard Chinese, but it seems to “make sense”. A low bar perhaps.
I’ve never heard anyone say 犯事情. Seems like a usage issue to me. Of course, 事情 can be used in a negative sense, like 事情大條了.
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Sure, it’s a usage issue indeed, but given the presence of 犯, there’s really only one conclusion to be drawn as far as its meaning.
Why are you asking this question @milkteapixie ?
Hope it’s not because 事情大條了. 
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