Re border checks- it is definitely NOT the status quo.
At the moment, as a member of the EU, we have strict border checks at Calais, for both Tunnel and Ferry Port. You have to go through checks twice, by the French and by the British Customs- before boarding. The infrastructure around both Tunnel access and Ferry Port access- is massive, very high fences, razor wire galore, and constant Police and CRS (armed SAS type police) 24/7 - stopping illegal migrants froms accessing either, and with PET passport checks- checks for import/export of food, substances, meat, live or otherwise, etc, etc.
They check cars randomly for illegal substances, possible drugs or terrorist linked substances, etc, 24/7- day in, day out.
All that will go post Brexit, unless with pay masses of money for this service - and there is physically no space, nor infrastructure in Kent for it to happen on our side.
And of course, we may choose to do no checks for stuff, people and beasts coming to us as imports - but the French will be totally withing their right to step up checks for anything and anyone coming from UK- people (be they tourists or business, hauliers, etc, etc). I really could NOT blame the French for going on go slow and extra checks. They have done it before, with very unplesant circumstances.