Liir's 'powers'
I'm doing this post for clarity's sake, because it will take a while to explain some things. Maguire is, while a wonderful author, one who likes to let you decide the exacts a lot of the time and while Liir got a whole book about him, there is still so much about him that wasn't explained in the least. Hence... this quick post on this specific subject.

Canon Proven Supernatural Abilities:

• can fly the broom: this is proved numerous times during Son of a Witch; Nor, Liir's half-sister can ride the broom as well so the criterion for this is unclear
  
• can pick up memories from people, places, and things: he heard the voices of the dead from the scraped faces, he picked up a vision of Elphaba rocking him in the onion basket cradle while he was at the mauntery, and he says during Wicked that objects 'talk' to him
  
• can will things back to life: after a horrible experience in Southstairs, Liir wills the life back into the broom; not only does the broom respond magically but the brush of the broom sprouts buds
  
• can make a broom fly: the broom was 'dead' after Elphaba's death, but after the aforementioned experience in Southstairs, the broom responds much like a mount
  
• can leave his body: while at Nether How, Liir floats above his body, to the point where he can see what a horrible haircut he has; while in this state, he can travel through time (the PAST) as well as space and can only been perceived (but not seen) by some; if this state is induced by trauma (as in certain parts of Son of a Witch), he can have trouble finding his way back to his body and require a guide (or music) to return ETA: there's evidence to support that he can slip behind someone's eyes and see what they see, but the specifics are unknown thank you Maguire ARGH.
  
• can hear the voices of the dead: as seen during the scene of Nastoya's restoration, he can 'hear' the voices of the scrapped faces
  
• can use the memories/souls/artron energy (for lack of a better term) to do things: while Candle's magic guided the ritual to restore Nastoya, nothing actually happened until Liir 'listened' and heard the lives of the scrapped faces
  
• has remarkable healing abilities: aside from spending three days in a well and not drowning, Liir fell from a serious height and the medical professionals on hand thought he would be dead within a couple of days, and that if he did recover (was not considered an actual option) he'd be either a cripple or a vegetable; Liir made a full recovery with little assistance from medicine or healing charms and that recovery would have been much quicker if his soul hadn't been wandering
  
• has some connection with dragons: stated vaguely at one point, as well as supported by the fact that the dragons attacked him when they weren't supposed to (according to their trainer) but did not kill him like every other target.
  

1. Liir has magic: judging by what's shown in canon, and by his mother, I've made the call that Liir has magic. Liir has rather powerful magic, in fact, though he has absolutely no training and seems to require some sort of 'guide' to do anything major (such as Candle's music during Nastoya's ritual). His magic will act subtly when he's faced with certain factors (music and high emotions tend to have an effect) but he will more than likely ignore it or think it positively common place. Also, it will never be anything but the smallest things. Anyone is welcome to notice that he's got magic, but he probably won't believe you.
   
2. Liir can see/manipulate/feel memory: all of his perception has to do with the past and he considers it his duty by the end of the book (he might come to that realization here) to 'remember' things, to record them, to keep them and to utilize the past (memory, really) the way it's meant to be used (in his opinion). That said, no piece of information/vision/memory will be nabbed from your pup unless there has been OOC communication to that effect; IC, it's hard to 'grab' from people because they're very much in the present, as much as they're made of memory in some ways so this shouldn't come up much. When it comes to objects, it will work the same (OOC communication with the owner pup's mun). When it comes to places, he might get brief flashes and glimpses of things tied to an area (a flash of someone fighting a troll at a troll statue), but if he's picking up something specific about anyone (such as with the example using his mother and the onion basket, of one specific person involved), the possibility will be discussed with the mun in question before anything is even HINTED. Anything bigger or more encompassing than that, which would only be for plot purposes anyway (I'm loving the game but slogging through the backlog regularly looking for stuff just isn't sensible), would be run past the mods by email.
   
3. Liir is not entirely human: this will probably never come up but, say, if the Judoon showed up and started scanning people, he would come up as not entirely human. I'm basing this on the draconian mentions, the fact that he's mentioned to be stronger than expected many times, the fact that we have no idea exactly what was up with the Wizard (his grandfather), and the advanced healing ability.