With the order of worship, there was actually a thread for posting that a while ago:
http://www.christianforums.com/t7742420/
As you can see, there's some variation, but it does tend toward a 'liturgy of prayers' structure.
One very general difference is that the translation of some of the prayers and rites in the liturgy will probably be extremely similar or identical to the ones from the Book of Common Prayer. As I understand it, there's some stylistic differences in the English between the translations used in Catholic and Anglican liturgies. Methodists would use the Anglican versions.
Methodists do ordain women, so that's another pretty big difference. It may not be the case that the parish in question has a female elder assigned to it, though, but the possibility is there.
Another thing you might notice is the presence of altar rails. While the usage or presence of these in Catholic parishes has declined since after Vatican II (at least according to Wikipedia), they've remained a common feature in Anglican, Methodist, and Lutheran parishes.
Likewise, whether or not the sanctuary is lined with stained glass windows is a case of individual architecture. Our family UMC does have them, illustrating scenes from the Gospels and maybe one or two from Acts (unfortunately, there aren't any good pictures of them I can find online; the single image from inside the Sanctuary that I could find is a rather poorly-lit and washed-out one from the church's website). I'm not sure if it was the windows, or something else about the Sanctuary and Narthex areas, but one of my grandparents' neighbors was a Catholic nun and at my cousin's wedding reception my grandmother took her on a tour. She remarked that it looked like it could be a Catholic parish, so the architectural and design elements may be very familiar.
As to a couple of the questions in the OP, yes, chances are really high that they'll be friendly to everyone, regardless of whether you're an 'outsider'. And while Methodists do practice Open Communion, I doubt it would be construed as disrespectful to not partake, especially given the circumstances.