Don't panic!
Wasn't aware that any of the Year 11 cohort were missing at any summer open evenings we attended. Usually the summer ones are for the selective schools and you wouldn't expect many of those pupils to be leaving at Year 11 end! Also, although you might think the Year 7s won't have settled in by the time the September/October open days/evenings happen, I think you would be very surprised not only at how quickly they seem to have adapted, but also as to how confident and knowledgeable about their school they are! We were shown round by Year 7s at more than one school we visited so that tells you how well they've settled in methinks.
Yes, I don't think any of the schools put a limit on how many times you can visit although it does get extraordinarily mentally draining doing all of those visits so bear that in mind! some of the selectives only have one open evening though so that's worth considering. The comprehensives on the other hand seem to have open days and evenings although you might have to book places by phone (more likely if you are visiting during the day)
I think some of the schools will also let you do another visit if your child has passed the exams and you are still considering it as a CAF option. We certainly did that for one of the grammar schools.
Yes, have noticed that more often than not the Heads are shying away from open Q&A sessions. But there are usually other sources of information available to 'tap' for answers and these are usually flagged up on any accompanying school literature you may be handed at the open days/evenings. Certainly a lot of the schools seem to have the Admissions Team on site to answer queries. And if all else fails you can email them....
I just think you need to be open and flexible and absorb the vibes you are getting from the pupils/teachers etc..... you won't really know what you are getting a feeling for at the first school, but by the time you have visited a few you will be able to tell virtually immediately. And your DC's opinion is very valid - if they and you can't imagine them fitting in well then don't even consider the school.
Good luck - we've just been through it and it was virtually a year of hard slog but as our DS now has the school he wants (and we wanted) we feel it's been worth it!