What is done for “Day Out With Thomas” when BEDT 15 is down for her, excuse me, HIS 1472 inspection. If I estimate correctly, her most recent one would have been 2013. How long does it take to do the inspection on such a small tank engine such as the 15?

Keep in mind that there is no such thing as a "typical" 1472 inspection. Strasburg happens to be quite good at them, given that they are one of - if not THE - best equipped steam shop in the country. Speaking from observation rather than experience, any locomotive regardless of size takes a long time to strip down, repair, reassemble, and test. Any other volunteer group might take years, but Strasburg has it down generally to a matter of months, depending on the urgency. Given that "Thomas" is still quite the cash cow, I'd expect it to be running as soon as the shop can get it out once it's due.