This surprised me a lot. I was under the impression that church law prescribes when to hold a service, up to the time at which it must be held - but maybe I am mixing this up with the prescribed prayer times in monasteries. Or maybe there is really such a prescription for Orthodox churches. I grew up in an Orthodox country, but as an atheist, so my knowledge is patchy.
Is there such a prescription?
Yes, there are such prescriptions for the Orthodox church, they are described by several books: generally Typika, then Triodion, and Pentecostarion, and for a few cases Octoechos, and Menaion. They contain the order of the services and prescribed time to do it.
Could an Orthodox priest decide to hold the same Sunday service twice in his church, if he wanted to?
There are a few restrictions on a service: the "Divine Liturgy" (Latin: the Mass) can be served only once per day in a single altar. And the priest can make "Divine Liturgy" only once per day. So, if you require to visit more than single Liturgy per a day, you should visit two churches (or two altars in the single church), with two different priest, but you can take part in Eucharist only once per the day too. The priest shouldn't serve the "Divine Liturgy" in the same church on multiple altars simultaneously.
As far as other services like the Hours, Vespers, Matins, the All-Night Vigil, Small Compline, Great Compline, the Midnight Office, the Moleben: I don't know specific restriction to make then more than once per day. However, it just have no sense.
They appear to offer the same content, just having different times so they can accommodate a larger audience with differing schedules.
Yes, if the church has more than one altar, and more than one priest in a state.