Augustine's City of God discusses this. Augustine's purpose in writing the work is to refute the idea, among pagans, that the embrace of Christianity and abandonment of the old gods is responsible for the catastrophes befalling Rome (as well as showing that the temporal fortunes of the Roman empire were of secondary importance compared to spiritual salvation anyway).

Certainly the Romans, especially in the West, but in the East too, were aware that they were going through very tough times. The Roman Empire had been through some pretty tough times before (the 200s, between about the death of Alexander Severus and the reign of Aurelian, were also a time of chaos). I can't say whether they regarded themselves as undergoing a string of catastrophes which, like the crisis of the 3rd century, would eventually be resolved, or whether they saw an irreversible deterioration in the Roman Empire's position.

You might find interesting this article written by Walter Goffart about Zosimus, a late 5th/early 6th century historian who wrote about the events of the 3rd to early 5th centuries. Goffart's basic argument is that Zosimus' work is probably the first text that articulates clearly, and tries to make sense in historical terms, of the fall of the Roman Empire.

Yes. Perhaps the best example can be found in Vegetius' De Re Militari, written sometime in the late 4th and early 5th Century for Emperor Valentinian (III?). In a section titled: Decay of the Legions, he writes:

The name of the legion remains indeed to this day in our armies, but its strength and substance are gone, since by the neglect of our predecessors, honors and preferments, which were formerly the recompenses of merit and long services, were to be attained only by interest and favor. Care is no longer taken to replace the soldiers, who after serving their full time, have received their discharges. The vacancies continually happening by sickness, discharges, desertion and various other casualties, if not supplied every year or even every month, must in time disable the most numerous army. Another cause of the weakness of our legions is that in them the soldiers find the duty hard, the arms heavy, the rewards distant and the discipline severe. To avoid these inconveniences, the young men enlist in the auxiliaries, where the service is less laborious and they have reason to expect more speedy recompenses.

Cato the Elder, who was often Consul and always victorious at the head of the armies, believed he should do his country more essential service by writing on military affairs, than by all his exploits in the field. For the consequences of brave actions are only temporary, while whatever is committed to writing for public good is of lasting benefit. Several others have followed his example, particularly Frontinus, whose elaborate works on this subject were so well received by the Emperor Trajan. These are the authors whose maxims and institutions I have undertaken to abridge in the most faithful and concise manner.

The expense of keeping up good or bad troops is the same; but it depends wholly on You, most August Emperor, to recover the excellent discipline of the ancients and to correct the abuses of later times. This is a reformation the advantages of which will be equally felt by ourselves and our posterity.

If you've never read it, I highly recommend reading Vegetius' work. He gives a fascinating overview of the Late Roman legions, comparing and contrasting them with the famed legions of the early Empire. Thankfully, an online version of De Re Militari can be found here.