The analyses of a sentence #1

The narrator recalls his childhood.
He has lived with his mother, Peggotty the only maid of his house, his stern stepfather Mr. Murdstone, and Mr. Mudstone's eccentric elder sister in his late father's house in Blunderstone.
Now, he was going to a boarding school near London on a coach, arrived a inn in the Whitechapel district whose name he doesn't exactly remeber, but nobody was waiting for him, contrary to expectations.
So he is waiting for somebody to take him to the school at the booking-office in the inn, thinking about the worst.

Supposing nobody should ever fetch me, how long would they consent to keep me there? Would they keep me long enough to spend seven shillings? Should I sleep at night in one of those wooden bins, with the other luggage, and wash myself at the pump in the yard in the morning, or should I be turned out every night, and expected to come again to be left till called for, when the office opened next day? Supposing there was no mistake in the case, and Mr. Murdstone had devised this plan to get rid of me, what should I do? If they allowed me to remain there until my seven shillings were spent, I couldn't hop to remain there when I began to starve. That would obviously be inconvenient and unpleasant to the customers, beside entailing on the Blue Whatever-it-was[the inn], the risk of funeral expenses.
[David Copperfield by Charles Dickens]
I'd like to know if "that" means "his starving to death."
I think "entailing" is a participle modifying "that," so I was wondering what role "beside" plays here.
And I'd like to know if "the risk" is an object of "entailing."
Thank you in advance for your help.