Let's say more than one strategy running and they all trade same stock symbol. Are the positions managed separately for each strategy?

Let's say more than one instance of the same strategy running but different account is assigned for each. Are the positions managed separately for each strategy and each account?

The reason why I'm asking these is because I think I got a problem when running the same strategy and the same stock symbol but two accounts (fidelity account and paper account).

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Are the positions managed separately for each strategy?

2 answers, and this assumes you're using only one account.

1. Yes. The sizes traded are determined by the Position sizing control.

2. However, if you select "Exit Orders should always exit the full Position currently held" in the Trading Options, then one script will exit the full position, regardless of the script or how you bought (or shorted) the stock, like using ATPro or fidelity.com

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Are the positions managed separately for each strategy and each account?

Yes, but you cannot use the same exact Strategy. If you want to do this, you need to make a copy of the Strategy, and assign each one to a different account. See User Guide: Reference > Dialogs > Strategy Explorer > Set Account...

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The reason why I'm asking these is because I think I got a problem when running the same strategy and the same stock symbol but two accounts (fidelity account and paper account).

You should be able to solve your problem using the information above and in the User Guide.

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The sizes traded are determined by the Position sizing control.

Even if the position size is the same but as long as the order date/time is different, each strategy can determine its own position correctly. Correct?

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you need to make a copy of the Strategy, and assign each one to a different account.

Nice idea!

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Even if the position size is the same but as long as the order date/time is different, each strategy can determine its own position correctly. Correct?

I don't follow you, but it's pretty simple.
If you don't select that "Exit Orders" option, then the sizes that WLP sends to Fidelity are the sizes of the Positions that you see in the script.

So, if you created an account Position with WLP and didn't change any settings, then the sizes should match those in your account - save partial fills, in which case the size for the exit order will automatically be reduced.