At this point in my life, I have no job and little income, and am falling behind on utility bills and mortgage. In order to keep my house and electricity, I'm thinking of using MS Word to print out a booklet of my lit-mag-published short stories and selling that to shore up my finances for a few months until I turn 62, and can start drawing Social Security. I don't intend to do a national marketing campaign or anything -- just offer the booklet to several friends and family members for a modest fee. Will the Business consider that self-published? Will it come back to bite me when I show my novel to an agent?
Yes, that's self-published. Anything you print up and offer to sell on the open market is considered published. Generally to sell on Amazon, you'll need an ISBN and having an ISBN means the book is published.
It probably won't hurt you, given that it's a collection of short stories, not a novel.
The real problem here is that you're undertaking something that requires real investment to do well, and it sounds like you're not planning on investing at all.
A quick MS Word document will look brutally ugly unless you really know what you're doing in terms of book production. Making a book look professional, or even attractive generally requires knowledge of book design, or hiring a book designer.
And I'm absolutely certain you've not run the numbers here if you think you're going to "shore up your finances" by selling books, any books.
If you list your book at $7.99, you retain about 70% of the proceeds or $5.59 for an electronic copy. For print books it's far less. You'll need to sell at least 100 ebooks to make a little more than $500. You'll need to sell 100 print books at somewhere north of $10 to earn $500.
I hate to be the bearer of bad tidings but most self-published books sell far fewer than 100 copies. The average number of copies for ALL self-pubbed books appears to be somewhere around 250, although I'm not sure that's still accurate. That means at least half of those published books sell fewer copies.
I say this not to discourage you, but if your house is at stake, you might want to spend your time doing something that has a more reasonable chance of earning income than self-publishing.