Car insurance: Sure, go ahead and save the £80. Although I don't know why you'd put the car back in your name after? Just leave it in his until there's some other reason it might need to change?
I think he's not wrong that giving her some independence on spending at 10 is a good thing. Some families do it with pocket money or birthday mondy. I have no idea what the return on premium bonds is so I'd mostly worry that she'd blow it. giving her a few pounds to spend independently is very different to having access to a few hundred quid.
Dishwasher - he sounds like my dad! For me, the dishwasher DOES save time because I can find 500 things to do while it's on and I think his approach is odd to consider the "dishwasher task" to take 3 hours. It doesn't. It takes the 10 minutes to load and the 10 minutes to unload and the time it's working is time to do other things. Also, I like a dishwasher because there is constant mess being generated in this house and this way, I don't have to wash up 5 x a day.
Private school... this one is INFURIATING. This theory is because Oxford and Cambridge have specifically said that they are trying to increase the proportion of children who attend from state schools. Lots of very privileged people are up in arms about their precious private school children being penalised.... Last time I checked the figures it was something like: 7% of the population attend private schools. At its peak, Oxbridge students were about 65% private school students. Subsequently, due to the significant effort oxbridge universities have made to reduce the proportion of private school students, it's around 35% or so (although there's also a large international student population).
What this means is that yes, it is NOT as easy to get into Oxbridge from private school as it used to be. But it is STILL significantly more likely to get in than from state school. Or, to look at it another way, a much higher proportion of private school students are accepted at Oxbrige vs the percentage of state school students who gain a place.