Rather than look at it by scenario, I'll look at this question by intervention:

• At what point to you offer advice?

  I'll offer advice at pretty much any point, although for homework questions I make an effort to avoid giving the question away. That's occasionally frustrating to both of us, when my friend wants to finish the damn question and I don't want to give away the answer, but it seems to work well in the end.

• At what point do you insist on pushing advice on them?

  I try to avoid pushing advice on people, since they usually end up fighting back and ignoring me rather than taking my advice, and it seems like a set-up for a later "I told you so". That said, if one of my friends is starting a serious project, with major implications to them (pass/fail, keep/lose job, etc), I don't mind offering unsolicited and sometimes unwanted advice.

• At what point do you grab their keyboard?

  When the project's failure (or degree of success) will affect others. If my friend's working at a different company, I probably can't do anything, but if they're working with me, I'll raise my concerns with our manager. (I have two things in my favour here: a clueful manager, and clueful co-workers!) The more severe the potential problems (and, admittedly, the more severe the consequences to me), the less likely I am to go through "proper channels".

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The hell with paco, vote for Erudil!
:wq