I didn't use the hose much; I just had it handy in case of "oopsies" and for that single rinse-out of my lye pitcher. I'd just dump it on the ground - it's such a tiny amount it never even discolored my grass. (And lye does occur naturally!)
I never worried about lye on my counter tops or in the sink as I started off using Red Devil brand drain opener as my source of lye - it was 99.9% pure lye which was perfect for soaping. Then meth became a huge problem and apparently lye is a main ingredient, and Red Devil stopped making their pure lye. So lye won't hurt most kitchen surfaces and may actually help clear your drains.
I worked outside mostly because of smells - my DH has a sensitive nose and I'd often make 2-3 different batches at once so the combinations of the different smells were often not so lovely, LOL. I did eventually get a hot plate for convenience but most of the time I'd just melt my oils inside and then bring them out - I do the "room temperature" method so I only added enough heat to melt my solid oils so it didn't take much. And then of course my oven (where I'd put the molds after pouring to force gel) is indoors so the soap ends up back inside at that point anyway! In the winter I'd do most soaping inside but I would
always mix my lye water outside. Those fumes are EVIL and the cold air would help cool it back down anyway.
Feel free to send me PM's! I'm a little rusty but it's coming back to me. Actually all this talk is really making me want to dig my stuff out and see how much of it is still good! It's been too long since I've donned my mad scientist lab coat, LOL.