Yes, earlier on, Yuki was intimidated on visiting Eiji (see her shifting eyes when she entered), but I believe that she's really just overjoyed about the song. The way I see it, it was her great dream to be singing like Rina, and now she's going to do just that with a song tailormade for her. At least, she said that she was happy herself - and I'm inclined to believe her.
Why Rina asked if it (not she) was alright - I think it's obvious that she was referring to the fact that Yuki had already halfway turned around and was going to leave without really saying goodbye to Touya. Remember the scene from episode 1? Turning around at the last moment and waving seems to be Yuki's normal way to part - it seems that she doesn't even RECOGNIZE that Touya might be hoping/wishing for something more meaningful. Rina immediately recognized that, and I believe she grabbed Rina's sleeve to indicate to her "hey, don't skip on the goodbye just because I'm around". And the fact that Yuki still didn't react will be seen as a sign that their relationship can't be all that deep (she didn't even know for sure that Yuki had a BF at all the day before).
Hidden agenda - maybe, probably, but the reactions here seemed to be rooted in what we already saw. Yuki is currently absorbed in her own world, and she sees Touya as a given, without a shred of doubt about their relationship. She DOES call him on her own, but she doesn't recognize his worries at all - and he's to blame about it too, since he sucks at communicating it. At the end of the episode, she's smiling at the telephone in her apartment (remember ep1? Where Akira mentioned that not having a phone installed in Yuki's apartment might be Yuki's employer's attempt to separate them? So the phone was probably just newly installed), and I'm almost willing to bet that she's going to call Touya - who happens to be talking to Rina at the moment.
"Hey, I tried calling you, but your line was busy - who was it?" is going to be an innocent landmine question in ep3, wanna bet?
