1) I would personally spell it "upper right-hand corner". It just looks better. In english we don't normally join more than two words with a "-". I would say "top right corner." I wouldn't use "rightmost", it just doesn't look right to me, though I suppose you could.
2) We tend to use these verbs interchangeably, though "Have you already had lunch?" and "I've cleaned up my room." is technically better. "I've cleaned up my room" implied I just did it, whereas "I cleaned up my room" could've been at any point in the past.
3) If you are saying that right now they're having a rough go of it "They seem to be having a rough go of it." If you're talking about what they've done prior to this point, "They seem to have had a rough go of it so far." Are they still having a rough go? Will they keep having a rough go? We can't tell from the second sentence.