If she is posted to the USA for a pre-determined, limited period of time in the context of her employment contract with her German university, her German health insurance cover will continue. If the period of time is not limited, German social security regulations will not apply to the stay in the USA. In this case she would have to take out private health insurance. Before travelling, she should clarify with her German health insurance provider if extra insurance should be taken out for her stay in the USA.
Apart from a local Portuguese health insurance company, you may want to consider a German foreign health insurance. Your German health insurance scheme is obliged to take you on again if you start working in Germany up to two months after your return or if you paid contributions for certain obligatory periods before leaving the scheme.
Form A1 certifies that foreign social security regulations are applicable in Belgium. In your particular case it is doubtful whether you are subject to obligatory social security in either Spain or Germany because this presupposes that you are working for a Spanish or German employer, for whom you would continue working in Belgium, and paying social security contributions. If this is not the case, neither the Spanish nor the Germans can issue form A1. Then the Belgian authorities would have to examine whether you are subject to obligatory social security in Belgium.
Q1: Do I have to return to the company health insurance scheme when I come back?
Q2: Is the scheme obliged to take me on again if my subsequent salary is over the limit for mandatory health insurance?
Even if your income is over the limit for mandatory health insurance, the company health insurance scheme is obliged to take you on again if you start working in Germany up to two months after your return or if you were insured for at least 24 months out of the five years prior to leaving the scheme or at least twelve consecutive months immediately before leaving the scheme.