I haven't had one so can't help with a lot of your questions but out plan is to let the pets (2 cats and 1 dog) roam around the house as usual - 1 cat will keep out of the way as she hates anything 'unusual' happening and doesn't like strangers. The dog will stay near-ish so she can check I'm ok, but won't want to be too close (next room probably). The other cat will be indifferent, or might watch from the kitchen worktop 
No other children so that's not a concern.
The midwives will bring gas & air with them. If I want pethidine, I can get it prescribed by my GP and have it in the house ready for MW's to administer, but they cannot bring it with them.
I'm having a pool - a rigid one. Significantly more expensive, but it has a heater (on thermostat) and filter, so can be set up in advance and no mad panic to fill or heat a pool, or attempt to maintain water temperature through a long labour. Also no fear of cats puncturing the pool!
We have a kitchen-diner, fairly open plan with just a breakfast bar dividing them. The pool is going to go in the dining room end - we have quarry tiles so no carpets to worry about. There is also a door straight into the garden (and drain) so the water pump can easily empty the pool straight down the drain. We also have a sofa-bed in the garden room next door, so will have that set up as a bed so I can nap in there if labour is long, or deliver on the if I want, or deliver placenta in there. There will be shower curtains and/or towels between the 2 rooms to protect the floor / speed up cleaning, but flooring is laminate so again easy to clean really.
I am choosing homebirth because of the lower risks to me and baby and the avoidance of falling into the 'chain of intervention' trap (the 'we'll just pop a monitor on' type, which means you're on the bed, which means poor birthing position, which means increased pain, which means more pain relief, which slows down labour, which means they get twitchy and want you on syntocinon, and keeps you on your back, etc etc often ending up with c-section).
I also know I'll feel more relaxed and rested in my own home, and won't be bunged on an understaffed, busy, noisy postnatal ward with everyone else's noisy babies! Selfishly, I'll have 2 midwives in attendance throughout my labour and birth and 1:1 support for a couple of hours after. No shift changes and random MWs I've never met, no worrying about people popping in and interrupting (even with good intentions) as I'm trying to focus, etc etc, There are loads of other reasons why I feel it's right for us and why I believe HB is the best option for a large proportion of low-risk pregnancies, but I think ultimately you have to feel comfortable with it - if you'd be more anxious without the anaesthetics and consultants immediately on hand, then HB would be a more stressful experience than hospital!