Based on Tanwen's observed lack of empathy, (along with pride, irresponsibleness, and manipulativeness)
here are the explanations I think make sense, and the implications they have for why she wants to hang out with us:
NOTE: these are not in any particular order. I am not saying which of these I think are more likely, nor which ones I think are better or worse for her/us.
Option 1: Tanwen is extremely racist, and doesn't see anyone other than changelings as people.
If this is true then it makes perfect sense for her to want to hang out with the "only" person here that she has met. It's even possible that all she wants out of hanging out with us is companionship. She probably sees us as either a friend or a possible friend. She probably is also capable of feeling empathy for us, just not for anyone else here.
Option 2: Tanwen is a sociopath.
This also fits with how she seems very impulsive, though that could easily just be part of her personality. If this is true then she probably has multiple goals here. She wants us to get more comfortable around her, and feel like she's our friend. If we care about her, then we will hesitate less to do something we wouldn't normally do (like cover for her after she kills someone) when she calls in the life debt. She may even get multiple uses out of us for smaller things, as well as the life debt. Having us as someone with a life debt AND who thinks of her as a friend is strictly better than having us as someone who has a life debt and distrusts her.
Furthermore, Tanwen might have a chance to observe some our abilities (or just ask us about them), which will help her determine just how useful we are and what she should use us for. This also gives her a chance to talk to us and try to make us distrust our friends. She can also try to stoke our paranoia about revealing to anyone that we are a Keeper of the Grey, possibly by telling us stories (whether true or not) about Keepers that she knew who were ostracized or abused for revealing what they were.
Option 3: Tanwen is the demon king, here to get the same training as heroes so that she can understand how to defeat and kill them better.
If this is true, then it's not all that different from the sociopath option (she may even be a sociopath as well as demon king). It does give a slightly higher chance of her having empathy, just not for heroes or heroes in training. Furthermore, she may be determining if she should recruit us to be one of her lieutenants eventually. Probably not, but maybe. It would be interesting.
Option 4: Tanwen is emotionally damaged, either from losing her team or from something that happened before that.
If this is the case, she may be putting on a strong front even though she does feel sorrow for her fallen comrades. It's possible that she really does have empathy, she is simply acting like she doesn't because it's the easiest way to avoid breaking down into tears. Her dead team is probably still out there, and she may want them to be pyred as a sign of respect and a way for her to grieve. It also allows her to hang out with Lirra.
Option 5: something completely different.
Implications: that I spent a whole bunch of time armchair psychologizing a character that just plain has different motivations and personality than I think she does, and that I don't really know all that much about yet? I know I said that I wouldn't say which I think is most likely, but by default it's probably this one.
), sociopath is the same as psychopath (just another name for it), and it's a combination of genes and experiences that causes it. I would differentiate between sociopathy and emotional damage in this case as an emotionally damaged person being damaged in a way that does not cause them to become a sociopath (ie: no narcissism, no extra impulsiveness beyond what they would have otherwise, and not having whatever other traits lead to a diagnosis of antisocial personality disorder a.k.a. Sociopathy). 
