Wow, a lot of people are expecting some new angry opponents lol. This is how I think about it:
Austria - Its UA is completely focussed on CS so it makes sense she's going for Diplomacy. I think her attitude will be neutral and protective for CS, except to those who compete her for CS influence. Those will probably feel her wrath. But somehow I do get the feeling from Theresa that she is not too reliable and won't mind to steal CS from you or start wars for whatever reason.
Byzantium - With its UA focussed on religion it makes sense that Theodora will put a lot of effort in that. So with that knowledge, it makes sense if she takes religious alliances very serious - being buddies with those with a common religion and hostile against those who don't. I expect her to back that up with her UUs to start crusades against others, and invest quite a bit in expanding her religion and stopping that of others.
Celts - Heavy reliable on religion so Bouddica will probably act similar as Theodora. With units that can gather faith by killing opponents, she's bound to be aggressive against most people with maybe the exception of those with a similar faith. At least the impression she gives at her introduction doesn't look very peaceful.
The Netherlands - Heavy dependable on trade and so will probably have a strong neutral or friendly attitude. Probably reliable and forgiving since holding a guarded or hostile attitude is going to affect its UA. Willem is probably going to be a sneaky opponent if he's against you, with a UU like the sea beggar. He'll probably get along with Adolphus quite well.
Ethiopia - Probably going to be a friendly and peaceful nation that will keep its borders limited, so you will not get a lot of diplomatic issues with them as long you do not have a warmonger attitude. I expect Selassie to be quite unforgiving due to their defensive attitude: he can afford to denounce others because of his powerful UA's. Those who dare to go to war against him will probably find out it is not worth the effort.
Carthage - Quite dependable on coastlines and connections, I expect Carthage to be more of a trading nation and so having more of a neutral attitude, perhaps a bit friendly. But Dido will probably also be competitive and not be afraid to go on warpath, or to take opportunities when presented. Will probably keep a significant army at her side.
Huns - Quite obvious what they are going to be. Attila is someone not to be trusted and probably ends up being hated by everyone else and finally being wiped out by either one or multiple civilizations. You kill them or they will kill you. Kind of similar like my experiences with Alexander.
Maya - Can kinda go into any direction, because none of its abilities are strictly directed towards something so it is hard to predict how they are going to be. I expect them to be quite varied, and to look into the possibilities of all available victories with perhaps a bit of a friendly attitude. Or they're going to be a second Pachacutti and be quite warmongering.
Sweden - Benefits the most from peace so will likely have a friendly and very reliable attitude. However, there has to be a reason why it has two UU, so I expect them to be quite aggressive against diplomatic opposition when competing for CS. I do not think that Adolphus and Theresa will get along with each other and end up combating one another for other CS' favour.