Invoicing: Xero Managing people: pick up Tom Peters, Little Big Things. Managing Projects: Getting Things Done & The Lazy Project Manager Managing Team Software: at your size you are small enough that can just talk and communicate. So something simple like BaseCamp & Weekly WIPS (work in progress meeting and bullet point list) will suffice. Then you want to evolve to something like ProWorkFlow / WorkFlowMax which provide the visibility, project management and time tracking.
Any questions email me ben@bwagy.com happy to help.
b) I keep track of sent invoices and paid invoices in a Google Docs Excel.
c) Aha, this is the big one :) First, as few meetings as possible. Second, manage by objectives & context, not tasks. Third, OKRs.
d) Not sure.