Here are my answers to your question to the best of my understanding:
1) The list of professions that are acceptable is
here (you've probably already seen it). Director/Manager/Personnel Officer of a VAT registered Company is on it, so your professional reference should be fine, and since your second referee has a British passport, that should also be fine.
2) As far as I know, you do not need to have a professional relationship with your professional referee—you just need someone who has professional standing to be willing to vouch for you. Both of my referees described our relationship as "friend of X years" on my form. The people at the Nationality Checking Service didn't even blink at the part. Of course, my application has just been sent, so it's entirely possible that something could go awry. However, nothing in the guidance says that you need to have worked with the professional referee. As long as both your referees have known you for at least three years, aren't related to you, and have not been convicted of an imprisonable offence, you should be in the clear.
3-4) The NCS service I used doesn't offer joint passport applications. However, they did send me a list of documents I would need for my appointment which specified which forms I needed to fill out. If you're confused, you might want to get in touch with them to double-check that
a) you can apply for a passport along with naturalisation using their service,
b) what forms you need to fill out, and
c) what supporting documents you'll need to bring to your appointment.
I will note that you and your will wife each need to fill out
Form AN—so you will have two copies to take with you. Make sure you read the guidance and the booklet at that link, as well as the form itself before you fill it out. I don't know about forms for minors, but it looks like you will need to fill out
Form MN1 on your child's behalf.
5)
I can't speak to the application form for minors. However, on my Form AN, my friends simply wrote "Friend of X years, Age: [Their age] years, Profession: [Their profession]" in the box provided. I can't promise that this is correct, but the person who checked my application at the NCS appointment didn't seem to think there was anything problematic about it.