On some level, there isn't a right or wrong, it's what you're both comfortable with. On the other hand, if you have totally different ideas on what you're comfortable with, then a problem is brewing.
For the OP who won't have a repair man in her home when she's alone, it's clearly her choice, but I couldn't live like that or date someone with those views. For example, if I had to stay home to chaperone her while the gardener came or the electrician, it would drive me insane and I would resent it. Similarly, if I were dating someone who said they'd never ride alone in a car with someone of the opposite gender that wouldn't bother me, but I wouldn't agree to be held to that standard.
One thing that strikes me as I read your post is that you don't know her friends and that bothers you, but you won't make the effort to meet them. I think that you either need to make the effort or accept that you don't know them.
As for her going out to dinner or to a concert, if this is someone who she's known for many years, I'd assume that if they had wanted to date they'd have done so by now. I wouldn't worry that suddenly they'd decide to date while you and she were dating. If it were a guy she had just met and she was planning a dinner alone with him and you weren't invited, that, to me, would be odd. For where I'd draw the line, for me, I'd draw the line at staying over night, in the same room. I think what I find a challenge her is that you don't want to be invited and won't go, but then are uncomfortable at not being there.
In any event, since you clearly have very different views, you need to sit down and discuss them and reach an agreement, and the sooner the better.