vppoulis To be clear, the new fields are for your company not for clients?
If you make any changes to the PHP files you won't lose the changes, but you won't be able to update until you change the files back. As far as changes to the database (new fields), it will likely cause some incompatibility with future updates.
Your proposed new fields (especially tax ID) are a great idea to boost the accounting side of ITFlow.
In regards to the order the fields are displayed, an invoice/report template system would probably be the best implementation of the feature.
Great suggestions, I'm sure the devs here will consider them.