The first one I believe I read either on avengerkink or norsekink. This is what I remember of it: it's an AU and before Thor's coronation, Odin told Loki that Loki was to be advisor to Thor, basically doing all the work and getting none of the credit. Loki didn't like it one bit and took off for another realm, leaving Thor to do things himself. Then some foreign dignitaries from another realm came to Asgard and Thor screwed up pretty badly by insulting people (including a female ambassador or something that he insisted on hitting on, despite her subtle attempts to get him to back off) and generally being bad at diplomacy. I think Thor confronted Loki at some point for abandoning him or making him look bad, I'm not really sure.
The second one I think is from AO3. I think it was a long story, most likely gen or Loki/Tony (and Thor/Jane), but the bit I remember is that Jane has gone to Asgard and she has to undergo some trials to be accepted there or be given the golden apples. There are 3 tests and Jane fails one (that I think involved something typically feminine she was not very good at) and passes one (that I think involved some kind of scientific principle). The last one (I think) was some kind of unsolvable problem Odin used so she'd fail for sure, and I think Thor and other people got pissed about that. And that's pretty much all I remember about it.
Thanks in advance.