I haven't used Zen Cart myself, but from reading their help, what I understand is this:
You can set up different geographical zones, and assign different tax classes to those zones.
So if you have a drop shipper in TX, set up a zone for TX and assign the sales tax rate for TX. If you have another drop shipper in AR, set up a one for AR and assign it a tax rate.
I assume people have to fill out a few details at checkout, like their country and state, so the software will use that data to automatically calculate their final total.
These articles will hopefully answer both your tax & shipping questions:
Tax
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Shipping
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