You cannot trade with factions you are at war with and they of course cannot trade with you - whether the route is blockaded or not.
blackboard is correct in that removing your ships or mutual borders (in other words breaking off all contact) will result in a ceasefire. Though this will not take immediate effect. You will have to end the turn first and then again in order for the game to register one entire year without contact. A ceasefire or desintegration of the faction in question is your only hope to re-establish trade.
"Local Trade" is not trade with neighbouring provinces over land, it is in fact a default income produce by the trader building and based on the values of trade goods in the province itself.
"Import tax" is a small percentage you make from rival factions' overseas trade with your faction. By default I think this is 20%.
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