It is clarified that solar eclipse and lunar eclipse are signs of ALLAH (swt) . On these occasions shariah has guided to indulge in salah (نماز), prayer (دعا) and seeking forgiveness (استغفار).
At the time of solar eclipse, offering two raka’at salah (نماز کسوف, eclipse prayer) is masnoon (مسنون), better is to offer with the community (جماعت), longer surahs be recited in it and to prolong the Ruku and Sujood (رکوع و سجود) and remain engaged in prayers (دعا) till the time of eclipse is over. Further, this prayer has neither Azan (ازان) nor Iqamah (اقامت).
Rest, the variety of thoughts amongst people about it (for e.g. advising a pregnant woman to be careful etc) have no basis in shariah law, however, if in opinion of doctors it is necessary to be careful, then there is no harm on acting upon their advice, but this is not the ruling of shariah. Therefore, if someone wants to act on it as a medical treatment, there is room available for them.