Quite right. Whom is used when it is the object of a preposition ("To whom it may concern") or verb ("The man whom we saw last night") or the subject of a complementary infinitive ("The person whom we took to be your father"). Who is used on all other occasions. [Penguin Reference Books]
Now is it...
boldly to go
to go boldly
to boldly go?
Exactly, good citation, or maybe just remember Hemingways's "For Whom The Bell Tolls"; shepherdcohen also puts it well.
As for "boldly to go", a bit of artistic licence may apply. Grammatically, strictly, or, dare I say, technically, the infinitive (to go) should not be split; however, it sounds better, when declaimed aloud, when it is split in this particular instance.
Re its, its', and it's, oh yes, that is a recurring problem. One of many. I'm a teacher - of history, and politics - among other hats which I've worn, and spelling errors in essays, assignments really annoys me. I'm more tolerant of exam papers; they are normally written under considerable stress). More recently, I've had trainee teachers unable to distinguish between "principle" and "principal" in assignments; heaven help them when writing letters seeking employment thus addressed.
(These days, most computers have spell check functions, and a lot of the students cannot even be bothered to click on the relevant key before submitting an assignment. More than once, I was even instructed by my then head of dept (who was slightly dyslexic himself, and possibly a bit sensitive on this point) to ignore spelling and grammar entirely, as the papers I graded were supposed to examine the students' grasp of politics. Fair enough. However, I'd argue that written English is supposed to be a common language of communication, and I expect (hoping that it is not too much to expect) that students will have mastered the ability to express themselves clearly, in plain prose.
Cheers.