It is easy to forget the way that duty and honour are themes that apply equally to other characters in the play apart from Elesin, though of course these themes are shown to centre on him and in particular his role as the King's horseman of ritually committing suicide to be with his king in the afterlife. However, it is worth considering how honour and duty equally impact characters such as Pilkings, although this is in a very different way. Note how this is made clear in teh conversation that the Resident has with Pilkings at the beginning of Scene Four, when news of the disturbance has reached the Resident during the visit of the Prince:
You should have kept me informed, Pilkings. You realise how disastrous it would have been if things had erupted while His Highness was here.
Part of the duty of Pilkings in his role is to make sure that the visit of the Prince is not disrupted in any way and that any such "disturbances" are kept contained and controlled without being brought to the attention of the royal visitor. This is why in Scene 5 he is keen to stress that the volume must be kept to a low level when the visitors see Elesin and converse with him about his dereliction of duty. Although it is in a very different from, the play indicates that Elesin is not the only character with certain responsibilities and duties that he has to fulfill.
To answer your last question first (only because it's a simple answer), Elesin is upset because the women have not clothed him in the traditional clothing of honour. Because he is going to die for honour and is being regarded as someone of honour, he needs to be treated as such, and one such important way, particularly by women, that this honour is given to him is through clothing him in special cloths.
Other characters to whom honour is important would be Pilkings, in particular. He is in a similar position as Elesin, as he needs to look good and appear honourable in front of the prince (like Elesin must for the king) and so on. Read over Pilkings' scenes, you should find a lot of desire for honour in his character. Hope that was helpful!