Hi! I can give these a shot. First, no, the comitatenses and palatini were not stationed in a similar way to the early Empire. Under the early Empire, as you rightly stated, the military was organised in a forward position along the frontiers, and the modus operandi was to attempt to maintain absolute territorial integrity by fighting Rome's enemies outside Rome's borders and thus denying the enemy entrance into the Empire's territory. This did not entirely work in practice, but it was the intention.

However, Augustus, who designed this system, was aware that he and the imperial administration were highly important, and without an army nearby, also highly vulnerable. So he created the Praetorian Guard, which, along with the Urban Cohorts, was stationed in and around Rome. They filled the dual roles of being a protective force for the emperor and as the core of a campaigning force. This internal army became increasingly important over the first two centuries of the Empire, and it was regularly expanded by subsequent emperors. Also, Septimius Severus was the first emperor to station an entire legion in Italy, which filled the same dual role. During and after the third century crises the internal armies became even more important to defend emperors from civil war or invasion, and they subsequently underwent a massive reform during the reigns of Diocletian and then Constantine. There are not adequate sources to concretely delineate exactly when and where the different changes happened, but after the death of Constantine we can establish what the new army looked like.

The comitatenses and palatini that you mentioned were garrisoned in key cities and the surrounding areas during the winter months. In the fourth century, these included, in the west: Paris, Trier, Rheims, Cologne, Milan, and Sirmium, and in the east: Constantinople (both sides of the Bosporus) and Antioch. These forces would garrison in the homes of civilians, a great burden and regular complaint of the civilian population, and exceptions to this duty were highly sought after. Come the campaign season (April/May to September/October) the soldiers would be gathered up by an emperor or regional general, called a magister militum, and be utilised to deal with any straggling winter-raiders, invading barbarian armies, or conduct a campaign of their own. Some years no major operations were conducted, and instead the armies would have perhaps engaged in the building of fortifications or small skirmishes and the like.

It would be remise, however, to forget the third part of the army, the ripenses, or later and more commonly used by historians, limitanei. Most estimates believes the limitanei comprised fifty to sixty percent of the Roman military, and they were still stationed on the frontier. Some of their duties, such as patrolling, manning fortifications, defending against small raids, warning of invasions, and controlling passage across the frontiers, matched the duties of the legions under the early Empire, but the limitanei were not intended to conduct the forward defense operations of the early imperial legions without support from the field armies.

As for your second question, I'm not totally certain either. The core and most important part of the Roman military was still the infantry, with the cavalry playing supporting roles on the flanks of the main body of infantry. Coming to mind, is the Battle of Strasbourg in 357, where the Roman left wing of cavalry uncovered hidden Alamanni, who were intending to ambush them. Instead the cavalry charged, springing the trap in their favour and driving the enemy off, while at the same time the Alamanni cavalry on the Roman right flank was victorious, and defeated the Roman cavalry there with the help of the Alamanni light infantry. The Battle of Adrianople in 378 has in the past oft been hailed as the beginning of the medieval triumph of cavalry over infantry, and even though the Gothic cavalry played a crucial role and successfully defeated the Roman cavalry, this theory has fallen out of favour lately.

Third, the numeri and foederati are very poorly documented, you won't be able to find a definitive answer. I wish we could have some sort of law or document that records the differences and when each should be used, but such evidence simply does not exist. They probably referred to barbarian groups organised in slightly different ways, but we also cannot discount the Roman propensity for simply using synonyms as much as possible. If a Roman author was finding they were writing the word foederati too often, they would be very likely to just substitute a word like numeri and assume the reader would be able to figure it out.

Fourth, also hard to say. Romans did not have a strict dictionary of terms when it comes to matters like this, although I will say that most historians believe the units designated as pseudocomitatenses during the late Empire may be fulfilling the role of the earlier vexillatio.

Fifth, I don't believe they were organised along separate lines, although I am not certain. The Notitia Dignitatum might be the best source for that answer. It is a list of all military commanders and the units under their command, created around the late fourth century for the eastern Empire, and the early fifth for the western Empire. I have never scoured it cover to cover, but I can't recall ever hearing about a unit with sappers/engineers designations. Most likely the sappers were a combination of purposefully recruited overseers with experience or training in these matters, and rank-and-file labour.

As for other sources, there are plenty. I persoanlly would highly recommend Edward Luttwak's The Grand Strategy of the Roman Empire. Get the recent 2016 edition and you will find a great bibliographic introduction, which basically details everyone who has published against Luttwak's ideas since the book first came out in the 1970s (which is a lot of people). You can also find reference to some people who have independently come to very similar conclusions to Luttwak, and follow those sources up for more information. I would also reccommend M. J. Nicasie's Twilight of Empire, it is an excellent and detailed look at the army and also has a fantastic bibliographic section. Finally, although encyclopedias often give annoyingly tantalizing bit of information but can never go into deep detail, Yann le Bohec is the editor of the recent The Encyclopedia of the Roman Army and I highly recommend it.

Feel free to hit me up with any other questions you have, I'll try my best to answer them.