The answer is Yes and No
The way our group registration works is that you enter the number in the group, then enter the data for each person in the group... member 1, member 2, etc. You can customize what data is requested from each member, including custom fields if you want.
If you do not want to do it this way, you could limit the event to only individual registrations, but just make a custom field (like a textarea box maybe) for the registrant to type in the names of the other people in the group. If you need to charge based on the number of people, you could use another custom field where they'd select the number of people (from a dropdown) and the price would be calculated based on their selection. The only catch with going this route is the count of number of registrants will only count ONE person when the individual registration is used. If you need it to follow the number of people for the sake of a capacity check, then you will need the group registration option. If this is not a concern, then just do the Individual as described.
Regarding the invoices... there is not an official invoice created BUT you can customize the confirmation email to act as an invoice. You can insert various tags into the email to pull in data, then put the text around the tags as needed. You could show what they registered for, how they chose to pay, the amount due, etc. Then of course the registrant can print the email and send that in.
Something else you might do is use the email attachments feature and attach a PDF invoice to the email. This could be created specifically for that event. If it is a flat fee, you could already have that filled in, then they just fill in their name and info and mail you a check. Just a possible option B for you
Hope this helps.
