I agree to "never lie" however there is lying, and there is "not volunteering too much info esp if its info they do not need to know." When i had my first homestudy, my then-nearly 10 yo son was still cosleeping much of the time. I did not volunteer that, he had his own room with a bed and it certainly didnt come up. If he was the type of kid to blurt it out i may have handled it differently. He was unschooling at the time, and i told the sw we were "homeschooling" (which is not a lie, unschooling is just a form of HSing) and i didnt want to give the impression we did school at home, so i said i HS "using a child-led, interest driven approach" or some such thing. There is a way to couch what you do in "social worker-ese" to make it more palatable to a worker who might be a little more mainstream. And i usually tried to sound very open to doing "whatever was best for the child" and stressed how flexible i was and how much i research different options etc.
You may be able to kind of gauge how open/non mainstream your worker is once you meet her. Then you will know how "open" you need to be. Again, dont hide anything, but just be careful how you phrase things.
Pets shouldnt be a big deal, but again, depends on the social worker and their prejudices. Usually they will want animals to be UTD on vaxes (for us, just the rabies was sufficient, as we do not vax our pets either.) i had two cats at the time, and an aquatic turtle and it was no big deal. If you had a particular breed that raised a red flag, or a type of animal that freaked them out they may want more proof of safety etc. You may get a worker thats asks you something like "what would you do if the child you adopt turns out to be allergic??"
I live in a very nonvax-friendly state and so saying we dont vax wasnt a huge deal, the doctor just mentioned that on the physical form.
With a pool, you may be required to have a fence, alarms, etc. Whatever the rules are where you live.
I think having fears about whether its the right thing to do is very normal. The homestudy is a fairly painless process even though everyone worries about it, cleans their house obsessively, etc. I found it kind of fun to talk to the worker about adoption for a few hours.
I adopted through foster care so my experience with an international homestudy is limited, although i suspect the process is similar.