I don't know the answer to your question, but 5/8" gypsum wallboard is not necessarily Type X or fire-code. 5/8" is just 5/8" unless it's marked firecode. You can can get 1/2" type x as well. just to clarify for you.

Thank You for responding! Well, there are two sets of stairs; one to the inside staircase, and one outside. Are you telling me I still need more exits? The bathroom would be on the staircase(s) side. I don't actually want to make a bedroom down there, although there is a closet if someone wanted one. The basement is partially finished with wormwood paneling, but it needs cosmetic updating. I'm not quite ready to deal with that, as I thought having a bathroom would make it easier to tackle that in the future. Does that make any difference, or is it just assumed the room would be a bedroom? How much am I shooting myself in the foot if I don't have a shower? I have room, but I'd rather keep the room for storage (metro shelving), which I need much more than a shower.

you may use test plug on the floor drain or cut it off and cap it. Then cement over it. For the utility sink drain cut it off below the floor and cap it, Fernco has rubber caps for varying pipe sizes. These should be readily available at any home improvement store

If you're asking where to drain the footing drains on the addition--to the sanitary or to a sump with a pump--you're asking the wrong party. Your municipality will have the answer. And the answer may be completely different from the original one in the 1940s. For instance, until the late 1990s, where I build you were required to drain the footers and the eavestroughs into the municipal storm sewer. For the last decade, you must divert it all to a sump and drain it back onto your own property.