No you have to make your own way but they will arrange a taxi to pick you up
St Paul on line 1 is also an option and they have an up escalator
Same distance to walk... maybe 5 minutes
Yes to CDG... not sure to ORY. Cost is 25 euros, I think
I am pretty sure there was a sign up in reception offering transfers from the hotel. Probably worth ringing them to check. It is reasonably easy to reach by Metro from either airport or Gare du Nord. Go to Hôtel de Ville on line 1 and then a ten minute walk.
Get an answer from France Louvre staff and past guests.