If you were arriving by train its 2 miles. But difficult walk. Best to book right in harpers ferry or use uber to get around cheaply. They have lovely looking places in town.
Per the answers above, please note that the free shuttle service takes you between historic Harper's Ferry (drop off point is less than a mile from the train station) and the main park entrance. However, the shuttle does not take you to the Clarion Inn, which is just up the road from the train station, but the hike would not be desirable if you are carrying a lot of luggage. The hotel (and park entrance) are also along a busy road, so that would not be a pleasant walk. I do not know if there are any connecting paths from the park to the hotel - I did not see them on the map, but there could be unofficial trails. Best to confirm in advance if you're interested in that possibility.
Sorry, I don't know.
The hotel is 2.2 miles from the train station in Harper's Ferry. You can park at the train station if you can find a spot. There is a charge to park in the lot. However, there is very limited parking just before you go into the train lot. Most people take the shuttle bus from the Harper's Ferry visitors center into town.
Get an answer from Clarion Inn Harpers Ferry staff and past guests.