If, a short while before sunrise, I find there isn't enough time for ghusl (full ritual ablution), and I think that performing full ghusl and wudu (partial ritual ablution) might cause the prayer to go out of its prescribed time, is it permissible to perform tayammum (dry ablution)? And if I cannot find dust/earth, is it permissible for me to pray in my current state? And if the time for ghusl is only sufficient for one of the spouses, and they cannot perform ghusl together due to low water pressure or their belief that their performing ghusl together would cause the prayer time to expire, what should they do?

Whoever wakes up in a state of ritual impurity (janabah) before the prayer time expires, and knows that if he performs ghusl (ritual bath), the time will expire, he must perform ghusl even if it leads to the expiration of the time. This is the opinion of the majority of scholars. However, if the time is very constricted, the spouses can perform ghusl together if possible, as Aisha did with the Prophet, peace and blessings be upon him. If the water is only enough for one of them, and the other cannot find water, then he should perform tayammum (dry ablution) and pray. Tayammum is valid using anything on the earth that is of the same kind as dust. If he cannot find either means of purification (water or dust), then there are specific rulings for that case.