In short, yes to both of your answers.

The theme system has incredibly uncertain origins. Some, such as Carl Ostrogorsky, attribute it to as early as Heraclius, while modern scholarship moreso believes that it was most likely really instituted in practice under Constans II. To my knowledge, there's no evidence of the term "theme" even until the reign of Nikephoros I, and it's possible that historians like Theophanes were simply describing the old system using the terms for the system they were using.

So to begin with, what is a theme? A theme, in short, is an army/region that was governed by a Strategos, who had supreme military authority in his area second only to the Emperor himself. These themes originally developed from the armies of the late Empire, and sort of divide Anatolia into 4. You have

The Opsikion- Governed the northwest area and was derived from the imperial retinue (Obsequium, in Latin

Thracesion- Governed the Southwest, and derived from the army of Thrace

Armeniacon - Governed the Northeast, and derived from the army of Armenia

Anatolikon - Governed the Southeast, and derived from the, you guessed it, army of Anatolia.

Now, why were they established? At the end of Heraclius's reign, it was clear to the Byzantines that they wouldn't be able to mount any major offensives. You have some campaigning in northern Syria, but the primary military objective was protecting Anatolia from the arab raids. These raids were massive, would often involve tens of thousands of troops, and were designed to inflict as much damage on the Byzantines as possible. The Byzantine response to this was the transformation of their old field/imperial army system into the Themata. Instead of having 4 armies that were levied from throughout the empire like the old Roman armies, the four existing armies were settled and its soldiers given land with the understanding that these soldiers would both contribute to defense but maintain the land. This system worked beautifully for a few reasons.

1- It ensured that the soldiers had a motivation to protect the land from the raiders, since it was their land.

2- And this one is the most important, it played off the strengths of the Byzantines for maximum benefit. Anatolia is hard to traverse due to its terrain, so it was hard for armies to maneuver in it, but also hard for armies to know where the enemy was. The Byzantines didn't have the manpower to confront the Arab armies outside of rare exceptions like Akroinon, but they did have enough manpower relative to the Arabs to prevent full absorption. The Arabs were expanding in all directions, dealing with large rebellions in Khorosan, and never were quite stable enough to launch a systematic conquest of Anatolia, so they sent the raids. A 10,000 man army might be enough to sack Tyana and Caesarea, but it wasn't enough to hold the land. Behind every mountain could be a theme army, so the Arabs weren't able to hold the land as a permanent conquest.

So this is why the Themes are operating. At the start of their existence, the civil administration continued on through the old provincial system, but over time due to the overwhelming importance of the themes, the administration began to operate through that framework, with the Theme eventually not only defining the army that was stationed in it, but the entirety of the "province," that the Strategos was responsible for.

So, in short, it was a system of defense based on semi-professional soldiers (generally, the troops would only take the field in response to raids or other important military manners and then would go back to being farmers) and eventually, due to their importance, they became the administrative units as well.

John Haldon has a very good book related to this topic, "Warfare, state, and society in the Byzantine world." Also, I don't generally recommend podcasts, but the History of Byzantium is generally a very good one and Robin does a very good description of the evolution of the Themata system throughout his episodes.

Of the various Byzantine topics, military organization and history is probably the one I'd describe myself as an "expert," at, so ask away for followup questions :)