Roman engineering was something very different from what we have today. There was not the kind of scientific study so common in the modern world, so you probably won't find clear inventors.

Arches, vaults, domes and concrete are probably the four most important elements of roman engineering, the first three pre-dated the romans, yet nobody before realized what you could built using those. There wasn't probably one roman guy that realized all the uses of the arch, it was a gradual discovery of how it works. Same thing for vaults and domes. You can see across the centuries a steady advancement in roman techniques, but it's hard to point them to individuals. Not least because we're talking about a time so long ago. Concrete was a roman invention, but again, its use was a gradual process. There wasn't a guy that invented concrete and then suddenly there was this new building material. What you have is across the centuries the romans getting better and better building with it, especially in the Imperial Period, which brings me to your second question.

Patronage was a huge deal in the Roman state. Some of the greatest works on Roman engineering were made by people that had imperial patronage. Apollodorus of Damascus is probably the best example, he was a roman engineer that was a favorite of Trajan and designed many projects for him, including the Forum of Trajan in Rome. But his relationship with Trajan's sucessor, Hadrian, wasn't good and he might even have been killed by the emperor.

But Apollodorus wasn't a researcher. He wasn't paid to develop things. He was a extremely talented engineering that had a great empirical knowledge of how structures work and through Trajan's patronage (and his talent) was able to build amazing buildings, some that used new techniques or a better use of an old one. You could say he invented the flying buttress for example, as a structural element that works exactly like them was used in Trajan's Market, but that was just a detail in a bigger structure. For him, he probably just thought he used an arch in a clever way to deal with the lateral thurst of a vault.

In short, you might say that there were invention during the roman times, but they were developed slowly. Probably you had one guy that "discovered" it, but didn't use that well. Then another one comes and use it better, and so on.