All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is due on you to perform the Friday prayer, and it is impermissible for you to remain behind and leave it except for a legitimate excuse. It is narrated by At-Tirmithi on the authority of Abu Al-Ja‘d Adh-Dhamri that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: “He who leaves three Friday prayers out of negligence, Allaah will put a seal over his heart.” According to the narration of Muslim, “Let those people stop leaving the Friday prayer, otherwise Allaah will put a seal on their hearts, and afterwards, they will be among the heedless."
Hence, that you work in a hospital is not a legitimate excuse for you to leave the Friday prayer, unless you fear that your absence will cause harm to the patients and there is no one to replace you on whom the Friday prayer is not due, in which case, we hope this will be a legitimate excuse for you to leave the Friday prayer.
In fact, the scholars mentioned some excuses that permit one to leave the Friday prayer, such as him nursing a patient or fearing for himself or his property.
On the other hand, it is not due on the fasting - or non-fasting - person to cover his head, nor is it due on one to remain in a state of ablution while fasting. Rather, it is favorable for him to maintain his ablution in general, whether or not he is fasting, based on the statement of the Prophet, sallallaahu ‘alayhi wa sallam, “and none but a believer maintains his ablution.” [Ibn Maajah]
Also, there is no blame on the fasting person to swallow his own saliva while fasting, since it is difficult to avoid that. Imaam An-Nawawi conveyed the consensus about that, saying: “To swallow one’s own saliva does not break the fast, by consensus.” According to the words of Ibn Qudaamah in his book “Al-Mughni”, “And that which one could hardly avoid, like swallowing his own saliva, does not break the fast, because it is difficult to avoid that. This is similar to the dust on the road and the dust rising from sifting the flour.”
For further benefit, see Fatwa 85147.
Allaah Knows best.