Basic concept of わかる is a process to make an uncertain thing clearer by using the subject's knowledge or experience, whereas 知る is to get new/unknown information from outside. Think about a math question. When the questioner asks 答えがわかりますか, they expect the addressee to solve the question and get the correct answer. On the other hand, if the question is 答えを知っていますか, the questioner asks if the addressee already knows the correct answer (e.g., the addressee has ever solved the same question before).
As for your examples, #1a can be used even for a case that the addressee has never seen the bag, for instance, there is a name tag on the bag that the questioner cannot read, but they expect that the addressee might be able to read it. #1b doesn't work well in this case since the questioner expect that the addressee might know the owner. The meanings of the two expressions are partially overlapping, so sometimes they are interchangeable, though.
2)
わかりません means that the schedule is uncertain, whereas 知りません suggests that whether the speaker will attend or not is decided by someone else, not the speaker. They just don't know their schedule. (Note that わかりません works well also in this case since it's "uncertain", too.)
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