How trade tariffs work

I only thought about this today (!)

is this right:

if we crash out of EU and have to pay tariffs for EU goods, then it’s an export duty charged by the EU countries at source. Do they keep the duty or pass it on to EU?

and then UK “ retaliates” by charging export tax on British goods exported to Europe?

but if we crash out we dont HAVE to charge export taxes do we, why would we? We write our own rules. Is it the case that EU countries are obliged to charge an import tax? Is that it?

so thinking about Trump’s trade war, I understand that more easily - US charges import duty and China responds in kind. Simple.

apols for being such a dork. 

Plus global trade rules (WTO rules) say you must treat everyone the same in the absence of a free trade deal. 

So EU would impose the same tarrifs on cars from the uk that it imposes on say china (in theory to balance lower wage costs of production in china) but if uk doesn't put any on eu it can't put on anyone else, i.e. us of china to balance say local subsidies etc.