EURL - Invoicing work done for U.S. and German offices of a U.S. based company

I have just created an EURL (in November, with a capitalization of 1000€), including having received my SIREN/SIRET and my TVA number.  The EURL has so far had no income and has submitted no invoices, and has incurred about 3000€ in expenses (which have been paid personally).  At this time, I expect to have only the one client with whom I am currently working.  My current activity is computer consulting for a U.S. company, but this company also has an office in Germany.  I have initially been working for the U.S. office as an individual, but they would like to switch my relationship with them to that of my EURL working for their German office.  When I met during the creation of the EURL with the avocats and an accountant, they seemed to think that it would be very difficult for me to invoice the U.S. company for the work that I have been doing as an individual before the EURL is set up.  I did not understand the difficulties that they seemed to be debating among themselves.  I have so far obtained permission to report to my employer the amount of my monthly invoices, but not actually submit the invoices (due to the above mentioned difficulty that I don’t understand).  They would like me to submit these invoices soon though (perhaps by the end of the year?).

Questions:

1. Why might it be considered to be difficult for me as an individual to invoice a U.S. company (independent of whether or not I also have an EURL)?
2. Should I anticipate any problems with invoicing (as an EURL) the U.S. company in USD ($) for the last few months work?  Should I use the same invoice format for both the U.S. and the German offices?
3. Can I have the U.S. invoices paid in USD ($) to a personal (U.S.) bank account, then transfer the amounts to the EURL account in France?
4. I assume that once the relationship is with the German office, it should be no problem for them to simply deposit my fees in Euro (€) directly to the French account for the EURL.  How is any required TVA submission handled in this case?