Sorry, forgot to answer this question. There are of course other rooms in Heroica Hall (such as the residences of the leaders and the servants), but they are not accessible to the public. The adventurers do not sleep there, but at inns or their own homes. The organization does not provide any equipment for the heroes either, but it does own ships and horses for travelling purposes. In general, think of the building as a guild house or a community center, to give you a better idea of it.
Of course you can change your character's appearance. I wish you would post a 100x100 pixel avatar for him, too, since the one I made for him will be wrong then.
Yes, and also post the required information to your signature. Just look at how the others have done it, if you're not sure.