As for 1 and 2, grammatically, both are correct. In my view, I usually use the 2 sentence in case I put the sentence '' There is your bag on the table '' into Japanese, while I think I tend to use the 1 sentence if I want to put a slight emphasis on something which can be seen on the table. But I suppose there is no big difference between them.
3. あなたの鞄が机の上に,(と) あなたの傘が机の下にあります。
4. 机の上にあなたの鞄が,(と) 机の下にあなたの傘があります。
Both sentences are correct and we use both sentences in the conversation without knowing the difference between them. I think in this case I put the words or phrases in the beginning of the sentence if I want to emphasize them. For example, if someone asks you, '' What can you see on the table ?'' , then you can say,「あなたの鞄が （机の上に) あります。」 And someone asks you, '' Do you know where my bag is ? '', then your answer might be 「机の上に (あなたの鞄が) あります」
My idea makes sense to you ?