I was recently baptized into the Orthodox Church, into a tiny congregation of about 10 people, without a proper church building.
Something I find confusing is the minutiae of what to do if I was to visit another Orthodox Church, because the exact way we do things in our tiny group is not going to be the same as in a proper large church. Also, I realize some of these things will probably differ between the different branches of Orthodoxy. Basically, I wish I knew the little details so that I don't feel stupid or like an outsider if I turn up one day at another church.
I have been to dozens of different churches across the globe, and no two did things exactly the same. Don't fall into phariseeism.
I have seen huge Cathedrals full of nominal/ethnic Orthodox, who haven't a clue on proper (one time at a certain church, the bishop was celebrating Vespers during the Dormition Fast. As he came out a number of parishoners (who did not attend services) offered him a hot dog from the cook out on the church lawn. This church was over a century old, and they were cradle Orthodox). Then I've been in tiny house Churches the EP or MoP would be proud to celebrate in.
Act as the Spirit, and your growth into Orthodoxy, moves you and you won't go wrong.
At a Pan-Orthodox service one year, a woman you evidently had been watching me and my sons, asked me if I was Russian. "No, Arab" I replied, and when she seemed shocked, I added "but I go to a Russian (actually OCA) Church." "I knew it," she said, identifying herself as Greek, "you do things right."
For example, if I'm visiting should I attempt to take communion if my local priest would have allowed me? (i.e. if I've been to confession according to the frequency we agreed on). If so, what is the procedure? Would I have to make contact before I even turn up, or would I talk to the altar boy during the service, or do I just front up and see what happens? If I have to make contact, how early in the service would I have to do it?
You should do him the courtesy of calling beforehand, and he can tell you. If you don't get to speak to him, ask someone to get an altar server/deacon to give the priest a heads up, so if he had an issue (after all, HE's bound to answer how and to whom he administers communion), it can be dealt with before you're before the chalice.
I you get to speak to him, you might ask him any tips on the local custodm, e.g. some parishes venerate the chalice after communing, some don't, some priests prefer you open wide and he drop Him in, others that you use the spoon, etc.
Same question again if I turned up at another sacramental event, such as blessing with oil.
Less a problem. Usually you will get to see how he is administering the oil, and most priests will assume (and it's not as big an issue as Eucharist) that you are Orthodox if you come to be anointed.
If I want to go to confession at a visited church, when are the times that priests normally hear them? I often find it hard to figure out what times even my priest is prepared to do it, and I have no idea what other churches do.
Varies widely. Don't expect every priest will hear right before DL.
Buying prosphera. What exactly do you ask for. What exactly do you do? Up to what point in the service can you do it? How do you get the bread back at the end? Again, the way we do it in our little group isn't like they do in cathedrals with the little stall at the front.
None of the parishes I've been to (3) did we ever buy prosphera, but I know (vaguely, and at a distance) that it is done. Why would you want the bread back? It is a GIFT, after all. Somehow I think that there is a legitamate use you are putting it to that I am not aware of.
Do many Orthodox visit other branches of Orthodoxy when they are away from home, or do they tend to stick in their own branch? I remember one girl in the Russian church who visited us and it sounded like she had also visited Serbian and maybe even Greek, but I've talked to others who seem to stick to visiting their own brand.
Many stick with the familiar. Others, like myself, go to different ones on the road to witness to the Catholicism and unity that is Orthodoxy.