yes, you can trade with rebels.
your province and the target province to trade with must both have ports. with each level of trader you have in your province the trade amount will increase. the target province doesn't need goods or a trader just a port. to build a trader you will need goods in your province. of course your province must have goods to start a trade route at all. if you are building your network of ships to the target provinces note how many ports you see off that sea zone. if you can put that next ship in a 2 port sea zone or a 4 port sea zone, pick the 4 port sea zone.
see ah dut's economics 101 paper with some percentage increases from traders.
https://forums.totalwar.org/vb/showthread.php?t=32726
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