Hi exotic, you sound very keen to get a response to your 7:05 post. I'll answer part of it anyway, by telling you how it works out for our family having HE children of different ages. Two girls, now aged 12 and 5.
My little one was very ill as a newborn and took up nearly all of my time for the first few months. I relied on family and friends, particularly the home ed network. Dd1 hardly reduced her level of outside activities at all during this time, she just went with other people instead of me. I'd done them favours in the past - I try never to go anywhere with just one kid if I can take somebody else's kids along too - so I had no hesitation asking them for help when we needed it.
Once dd2 was out of the hospital and things had settled down we carried on with lift-sharing and childcare swaps as we always had. It's very common in our circle. At a given home ed group roughly a third of the children will have come with a family other than their own. Sometimes they get a lift home with yet another family!
While the three of us were at home together, I saw the big age gap as a bonus because the kids' needs were different. I played Monopoly or chess with dd1 while feeding the baby. Dd1 often moved my game pieces when my hands were full. Or I used a bookstand with clamp to hold the book I was reading aloud to dd1 while cuddling the baby. Easier than having a toddler clamouring to be in your lap or needing help with the potty when the baby needs to be in your arms!!
Like most parents, whatever the age gap, I had worried that dd1 would miss out on my attention when I was occupied with the baby. She certainly did get less of my attention than she'd had when she was an only child. But the fact that I was on hand throughout the day meant that the little bits of attention she got from me here and there added up to enough for her, which probably wouldn't have been the case if she'd been home with me for just a few hours a day. To my surprise, she was hardly jealous at all. Schoolchildren with baby siblings have to fight for mum's attention during the short time when they are with her - which unfortunately often includes the time when the whole family is overtired and ratty. That evening "witching hour" when baby is fussing and mum is trying to get dinner on the table isn't great for spending quality time with an older child. By contrast, if the older child has also had access to mum during the baby's happy mornings and throughout every nap, she'll have had plenty of attention already and is willing to occupy herself for a while in the evening.
Toddler groups and all that - yes, dd1 went to some of those. I always left it up to her. Sometimes she'd read in the corner, sometimes she'd play with the little kids, sometimes she'd play with the baby toys or do art by herself. I think older children often like the opportunity to do little-kid things. Having a little sibling provides the ideal excuse for an occasional return to Duplo and playdough. If I enjoy feeding the ducks sometimes, why wouldn't a nine year old? This is no deprivation. They still do big-kid stuff at other times.
My daughter also had the option of staying home alone whenever she wanted. Leaving older children home alone seems to be more common among my HE friends than it is with schoolchildren. Lots of reasons, I think. Necessity nudges some people in that direction, perhaps. We knew our elderly neighbours very closely because we were around so much, so dd would have gone to them in an emergency. We have the time to spend coaching our children in what to do in various situations and they've seen mum dealing with plumbing emergencies and maybe even helping. My SIL argues that it's dangerous to leave a 14yo home alone, citing the case of a local girl who was left home alone for the first time at that age, tried to boil the kettle, couldn't work out how to light the gas, and gave up, leaving the gas on. She didn't recognise the smell of gas which soon filled the house or know what to do about it. Mum arrived home and saved the day, and no longer leaves her daughter home alone. I draw a different conclusion: kids who don't spend much time at home WITH their parents getting the necessary life experience to handle a range of situations are ill-prepared to spend time at home WITHOUT their parents.
HE parents have more opportunity to observe how their kids respond in a range of situations so perhaps we feel better able to predict what they can cope with. It used to surprise me to see posts on parenting forums asking "Is it safe for me to let my nine year old do xyz?" and I thought "how can you not know what your own child can handle? Why ask strangers? You LIVE with him, we don't!" Then I realised that spending far less time with a child does equate to knowing him less well and maybe being unsure of how he'll respond, so some people do rely on what everyone else is doing for guidance.
My little one generally enjoys going along to her big sister's activities. There are often other younger siblings on the side at the hockey match and they all mill around playing together. Or we bring a stack of books or toys and sit together reading or playing, and she likes that attention. Dd1 gets to many of her own activities under her own steam and roams all over the city by bus so I'm not a total taxi service anymore, and that eases things considerably.
So yes, I love this big age gap and I don't think it interferes with our home education at all. I wouldn't have it any other way!