1. Can I change the labels to suit my client's needs without affecting any CBS current or future functionality - I am assuming yes
Yes, you can change their text. Changing their text (label) has no affect on their values stored.
2. Can I change the number of options that display - I am assuming no (without code hacking), but that I can replace a label with a space or two
Yes, edit the below XML file and add more options to manual_payment_type. As I understand it's 100% cosmetic you can add as many as you want or flat out edit the existing ones.
/components/com_comprofiler/plugin/user/plug_cbpaidsubscriptions/xml/edit.front.recordpayment.xml
3. What is the difference conceptually between Gateway account, payment using and payment type?
Gateway Account = payment gateway used (as seen in CBSubs > Gateways)
Payment Using = the method the user paid (some gateways may have multiple methods)
Payment Type = the type the user paid with (only 2 options I believe atm: Credit Card or Offline)