As someone not from the UK (Canadian here), I find I am struggling to understand these kinds of phrases as we don't word things quite that way. Does "Mairi is just x-ing" mean she is in the process of doing it right now, or she just finished doing it a moment ago, or she is about to do it, or what? I have a British coworker I normally ask these things but since we are all isolating at home, I have no one to ask!
Usually "is just xing" = "in the process of xing". You might say "Mairi is just coming" in a meeting, etc. to mean "(we'll hold off starting for a moment as I believe) Mairi is about to arrive". "Has just x-ed" = finished doing x a moment ago. "Just x-ed" = just did x a moment ago.
In many contexts "just" can also mean "only", to downplay the importance of the activity. Depending on context and intonation "Sarah is just finishing her Duolingo lessons now" can mean "Sarah is in the process of finishing her Duolingo lessons now (so she'll be ready for a chat in a minute and I won't interrupt her)" or "Sarah is not doing anything more important than finishing her Duolingo lessons, so I can definitely interrupt her for a chat".
"Just" as an importance reducer can also be used as a form of politeness that (paradoxically) does not at all imply that the task is not important - this and the use of diminutives are quite common ways of being polite in Scotland - "could you just give me a wee hand with this" does not imply that you won't appreciate the help you're asking for or are downplaying the imposition you are attempting to place on the person you're talking to.
Yes, that's usually the case. There are a few Gaelic names that are commonly found in Scotland in an anglicised form (Màiri => Mairi, Catrìona => Catriona, Iain => Ian, Alasdair => Alistair/Alastair, etc.), so a Màiri might call herself Mairi or Mary in English, likewise Catrìona/Catriona/Catherine, Iain/Ian/John, Alasdair/Alistair/Alastair/Alexander (the section on Names gives both Mairi and Mary as English versions of Màiri, so either should be accepted in the answers).